If it's a post-WW2 scenario for this union, I can't realistically see a merging of armed forces, but a very tight shared command (NATO style++) is more likely.
Defence is the most fundamental role of a state.
Only the author can rule on these questions, but frankly I think by far the strongest reason to consider having any Union, and certainly one that has elaborations like a population-proportional popular legislature to govern the Union, and a Union President, would of course precisely be to bulk up Scandinavia as a player in world affairs, and very much exactly to get a strong collective defense.
Thus, defense as basis of nationhood is a two edged sword. In an earlier draft of a response to your remarks here, I rather dialectically came to the tentative conclusion that indeed on paper, the constituent nations of the Union should indeed have military force apportioned formally to them, under the separate sovereignty of their various states. But my major consideration was not so much formal arguments about sovereignty but rather linguistic. I do not know to what degree Norwegian, Danish and Swedish are mutually intelligible to the respective peoples of each nation in practice, but certainly the languages are distinct and any Danish soldier or sailor trying to correctly understand orders in Swedish or Norwegian must be pretty well trained to remember to take note of the words that are different. I favored the idea of a single unified set of armed forces for the whole Union, but then the question of language becomes more pointed. The logical common language of reference should be Swedish I think, especially if Finland ever joining is in the cards--native Suomi speakers mostly understand Swedish, or a dialect of it, pretty well I think, whereas Suomi is a very different language, not even Indo-European--Finns and Estonians would understand each other pretty well I think, but no one else would unless they studied and trained in the common Suomi roots, and dialect differences might still trip up someone indifferently familiar with either. Well, I think the Danes and Norwegians, who put together outnumber the Swedes a bit, would resent having to use Swedish exclusively. Having separate forces for each nation means that each force uses mainly the common language of their kingdom or republic, and then perhaps getting everyone at least passably competent in formalized military command Swedish might be easier to swallow.
So I guess I come around to your concept of several separate parallel commands, but in practice the point of having a Union is to maximize effectiveness by common policy, doctrine and equipment. The coordination between the national forces must be quite tight, and
de facto the combined forces will operate as one. Above the supreme commands of each force for each nation, must be a Union supreme command, which on paper is a federal alliance, but in operational practice is unified. Rank insignia must be clear at a glance, command in serious operations must seamlessly leap across national lines. The separation then is largely symbolic, and boils down in operations to forces recruited from different nations generally serving together and largely separate from other Union national forces.
But never entirely! Let's visualize the situation should we achieve what I think is maximal extension and devolution of component nations. Supposing Greenland and the Faeroes are formally separated from Denmark and tiny Union republics in their own right, Iceland joined initially or sometime during the Cold War anyway, and after some major collapse of the Soviet hegemony over east Europe (which might not involve the collapse of the Soviet Communist party rule and the continued existence of a version of the USSR--I'll just call it Russia though to distinguish from the Cold War USSR, whether it still contains Ukraine, the central Asian republics, the Caucasian ones and so on or not) Russia will still, in any scenario that does not involve a major nuclear exchange, remain a very strong power at least in northern European theaters. Conciliating them, especially if they make concessions such as letting the Baltic Republics go (as a continuing Soviet Union ought to, provided they can be satisfied as to security--the Baltic peoples deeply resented Soviet Russian rule) is going to be important. Let's say we have all four Baltic coastal states joining as separate Union nations, so the count of total nations, big and tiny (in population/wealth terms) comes to ten. We have Greenland, Iceland, Faeroes, Norway, Denmark, Sweden, Finland, Lithuania, Latvia, Estonia. In a post-Cold War situation, what is a rational deployment of forces?
Russia remains an enigma--potentially able to turn into a powerful aggressor again, the Union must be preoccupied with plans to defend all territories against Russian expansionism. The four Baltic coastal eastern republics are on the front line; in a world disregarding deterrence and diplomacy and relying on force alone, these should be armed to the hilt. But even massive fortification of these four nations cannot be a guarantee against Russian conquest; Russia is just plain big, and hard to defeat due to its great strategic depth (even lacking the entire southern tier of Soviet Republics)! The key to defense of the vulnerable Baltic east is a bit paradoxically, diplomacy and deterrence. The Russians even in general collapse are going to be potentially strong enough to assert major security concerns and refuse to loosen their effective grip of terror on the east Baltics unless they are satisfied their security from that direction is otherwise assured. The way to otherwise assure it is to continue the Cold War de facto stalemate in Finland. Finland, as a condition of not being absorbed into the Soviet system wholesale, agreed tacitly to be inoffensive, to maintain only a small military and avoid provoking the Bear. Now just in joining the Union they are being more assertive--but if the entire Russian border, including perhaps the northeastern province of Norway, are largely demilitarized, and if the Western powers have enough leverage to make this mutual as it was not in the Cold War, and assert the right of inspectors to verify low levels of Russian concentration of force at some depth beyond the Baltic republic borders too, so we have Russian inspectors roaming around the four former Soviet sphere of interest republics verifying limited presence of force there, and Union inspectors roaming a comparable depth of the Russian border zone also confirming low concentrations of Russian force there, we have a stabilized situation. Either side can violate the agreement and rush forces in from their respective "rears" but if they try it, the inspectors will sound the alarm--arresting, still worse killing, the inspectors would be an act of war in itself. Such a reckless move would quite likely trigger general Armageddon; that's deterrence.
So the four Baltic nations, on paper, maintain their own uniformed forces in the Union--but these are tiny. However, each republic pays into the general Union defense budget to a comparable degree, based on per capita national wealth average, to what the unrestricted six nations pay, in combined national and Union payments, and citizens of the four Baltic nations may volunteer to serve under one of the other six national banners--this means Baltic people must learn one of the western Nordic languages of course--since everyone in any uniform in the Union is under some pressure to speak Swedish to a fair degree for command purposes, a lot of them would go to the Swedish forces, which are their nearest destination anyway, and the logical base for reserve forces to rush into Finland and the southern small republics in an emergency. But others might choose to join Danish, Norwegian, or in theory one of the Atlantic small national forces instead. They still have to learn Swedish, and now Danish or one of the Atlantic national languages too. In theory each of these Baltic expatriate volunteers is in the service of whatever crown or Republic they enlist with, but any national force hosting lots of Lithuanians or Latvians is going to form corps to put most of them in, rotating individuals to national dominated units for general cross-national familiarization and training in specific operations, then back to their de facto exile forces, where they are understood to be ready reserves to rush into their homelands. In case of deteriorating relations with Russia, where the Russians start fortifying their borderlands and perhaps expel the inspectors, but the Union and Russia avoid starting open war, the nominal Baltic republic forces can be built up overnight, as their respective "emigre" volunteers come home in force to be reorganized into formally local units on the front line. Whether they get formally disbanded and largely sent back west depends on how diplomacy proceeds with the Russians after that. Hopefully this situation never arises, as it would be one hair trigger away from general interbloc nuclear war.
To the west, Sweden is the logical base for sea and air power over the Baltic, until we come to Danish waters anyway, and being in close confederal cooperation, in fact the Danish and Swedish naval units and air units will interpenetrate each others' formal waters and air space quite freely, with Union command overseeing both. These naval and air forces will have lots of Baltic service members, in the air, at sea, in ports and at airfields, each under one crown or the other. The ships and bases will in fact be multilingual. The token, limited complement and kit forces in the eastern republics will have logistical capabilities far outstripping the local force in being, in pointed readiness to suddenly host a whole lot of "expeditionary" forces each of which by amazing coincidence happen to include majorities of locals, and formally transferring their allegiance to their home republic forces will be a major diplomatic signal of big trouble for Russia.
Generally, there would be no reason for Swedish naval or air units to operate in the Atlantic, but a portion will be exchanged with the Norwegian (and tiny token Icelandic and still more desultory Faeroe and Greenland nominal forces) for familiarization and general proficiency. The Danes are poised between Baltic and Atlantic and thus share a portion of both routinely. Norway takes major point in the Atlantic, especially north of the Skagerrak outlet, but again they will trade some task forces with Swedes and Danes, swapping their units into the Baltic again for general familiarization and practice in specialized skills. The three tiny Atlantic island republics will have really tiny forces on paper, and these mostly specialized for utility "coast guard" type duties--revenue control and general policing, and search and rescue--but will be subsidized by the Union to have some token major units, which operate effectively under Norwegian dominated command on Union defense duties.
On land, the three major kingdoms will maintain armies which, reinforced by Baltic citizen volunteers rotating between their own linguistic units and kingdom ones, in combination are geared to give the Baltic borders a strong and tenacious defense. The Finnish republican force is smaller per capita than the Baltics, because all the western kingdoms, including token volunteers from the Atlantic islands, rotate in small units for training and familiarization--a lot more Finns are armed and in uniform than those formally mustered into the Finnish Army, because a large number are there temporarily on a rotating basis in other uniforms. These put together with the actual Swedes, Danes, Norwegian (and handfuls of Atlantic island troops) who are present in Finland at any one time count toward the treaty cap on armed presence--but arms, in caches where the Russian inspectors are guaranteed to be able to watch but unable to interfere, are also stocked in place beyond routine training and standby presence, and behold, lots of Finns have volunteered in Finnish or western kingdom uniforms, served a stint, and are now enrolled as Finnish reserves. The Russians really should think twice about starting anything!
Keeping such reserves in the southern Baltics is more provocative to Russia, so these republics are more exposed, except that they do maintain forward air bases far beyond their nominal requirements. The main defense of the Baltics is their veteran reserves plus the general tripwire deterrence--Russian forces can easily conquer the Baltics, but they are sure to then be in general war with all the Union, under pressure on the entire Finnish-Norwegian frontier, Russian shipping being ruthlessly hunted by the cooperating Union navies.
Should the Union have a nuclear deterrent of its own? I think yes, they surely would if the Union did not join NATO, and possibly no, they might not if they did join NATO in its formation or soon after--delaying this as late as 1960 probably means the Union joins the nuclear club. Nuclear weapons would break down into strategic forces, which would be a mix of land based IRBMs and submarine launched missiles--even if making actual nuclear powered boomers is beyond the Union's paygrade, OTL the Swedes have developed remarkably good air independent subs using chemical fuel, and that is good for short range hiding small subs in the Baltic, and perhaps for Norwegian ones operating within a few hundred miles of the Norwegian/Union coast in the north Atlantic and Arctic. Perhaps the Union would decide not to develop "tactical" nukes, and if they did, their most logical applications are air interceptor AAMs (like the USAF Genie missile) and submarine torpedoes--using "tactical" nukes on the battlefield is lighting the match for general nuclear exchange after all. Certainly strategic nuke forces--missile bases and boomer subs--should not be separate kingdom units, formally--de facto each base and vessel will have some dominant language and practical closer affiliation to some nation or other, but legally speaking strategic use of nukes should be under strong central Union command, and obviously a last resort.
If they join NATO early, the Union will probably be dissuaded from developing Union nuclear weapon capability, but perhaps might be encouraged to go beyond chemical AIP to have Union nuclear subs, and if the Union is persuaded to join long range expeditions, under NATO, or in other multilateral alliances such as SEATO, or as UN mandate forces, perhaps even nuclear powered surface vessels--this would involve major subsidies as well as strategic security agreements and permissions from Uncle Sam. The Union does not require nuclear attack subs in the Baltic, but might want some in the Atlantic off Norway.
All nations except the eastern four maintain air forces comparable in per capita wealth, and the latter of course contribute lump sum funds and a flow of volunteers seconded to the western six nations (practically speaking, four, with Iceland getting very few) for training, integrated operations, and then placement in emigre squadrons within each kingdom/republic air force. Air forces are very mobile, provided common infrastructure and equipment is agreed to, and would be the first to be rushed into the Baltics should a crisis with Russia start blowing up.
In this framework then, there generally are no "Union" forces, except possibly for strategic nuclear forces, and I think it would be diplomatically astute to make any Union inspectors in Russia Union formally. Otherwise all uniformed personnel of all forces are under one national flag or another. But they mix up their training and practice operations and any UN or other alliance deployments a lot, and their weapons and doctrines and logistical chains are all closely coordinated by Union command. Everyone speaks a bit of Swedish, and enlisted persons and officers with serious career aspirations learn it well, though within their routine national force operations they usually speak the national language or in case of dealing with emigre Baltic units, their language.
Will the armed forces of the member countries be merged?
Initially I thought, sure, of course, but upon reflection, as in my answer to Devvy above, I guess not--on paper, they remain separate and usually operating in respective national languages. The formal separation makes swallowing Swedish as the de facto common command language less difficult for the non-Swedes.
In practice, as noted, it is necessary for the "separate" national forces to think and plan and practice in close cooperation with the others.
Scandinavia's population is about 2½ time larger than Sweden's and they have similar per capita GNPs.
If the Scandinavian armed forces are based on Sweden's there would be a considerable economies of scale because a lot of her military equipment was designed and built in Sweden.
Again the question of NATO involvement comes into play.
You are doing a fine job of estimating what could be the force levels for the three kingdoms if they adopt collectively basically a Greater Sweden policy of formal neutrality that is in fact armed strongly against the Soviets, and pragmatically in informal alliance with NATO. Refusing to enter NATO gives them maximum ability to see to it the pork barrel benefits of military buildup stay in the Union and maximally benefit Scandinavian industry and interests--the flip side is, joining with NATO might be seen to achieve higher security and possible access to US aid. And I think that given the high quality of Scandinavian designs OTL, especially postwar Swedish aircraft (by SAAB), the Union could swing NATO general procurement of some of their systems stretching the market for some systems a lot further--but at the cost of losing out in competition and having to adopt some foreign made systems, American, British, French or eventually perhaps German or Italian. Actually OTL the Swedes have procured some of their kit from various other European nations, so having to do some as NATO members is actually not that big a shift.
I think it is six of one half a dozen of the other overall, given Scandinavia's collective bargaining power, particularly if Iceland is in the Union too. Aggressive American firms will be somewhat reined in by State Department and DoD interests who want to keep the Scandinavians sweet on US basing in Iceland and Greenland and forward presence in Scandinavia itself. And the Union might be aided in achieving some ATL proficiencies such as naval nuclear power plants, and my respect for their engineering is such I daresay they might offer up an improved design that they can license back to American and other Western power firms.
Assuming WW2 goes like OTL, then Finland will likely stay out of the Scandinavian union due to it's treaty with the Soviet Union.
It isn't the paper treaty so much as the "correlation of forces" as Leninist dogma puts it. Russia is big, Finland is small, and when Red Army forces were rolling back the Axis ones toward Finland again, the Finns were in a hell of a position, without the western Allies having a strong case to rein in the Bear since Finland had legally speaking joined the Axis and helped attack the USSR. Later as the Cold War heated up, Western interests would like to "rescue" Finland from Soviet power, but doing so too overtly would likely trigger an unwanted WWIII; the OTL solution was not a terrible one for the Finns, nor bad for Russians or Westerners.
It is these realities, whether written down on paper or not, that would prevent any serious proposal to add Finland to the Union any time between the later '40s and the eventual collapse of Soviet power, probably around the late '80s-mid'90s as OTL. Conceivably, if the SU stays out of NATO and then adopts a much more Soviet friendly foreign policy than seems likely to me, they might get some kind of neutralized Finland deal out of the Soviets, but even if the Soviet regime agrees to mutual inspection on paper, it would be awfully hard to get compliance; the Union would have a bleeding wound they cannot bandage in Finland being basically held hostage.
Nor is it obvious that even if we have a collapse as OTL, that Russia will relent in objections to any Baltic republic joining. I optimistically proposed they might, to explore what a Finland within the Union might look like. I am not saying it is highly likely to be allowed though.
Will the Scandinavian languages be more similar than in OTL?
I think that to get the Union, the nationalistic preferences of the various nations would have to be catered to and reassured. Far from seeking to form a common Union language officially, the constitution will affirm that separate national languages are a national right, and each nation will maintain separate formal standards quite jealously.
All that is as far as official policy goes! But languages are not mere tools of central elites; they form and evolve dialectically, and grassroots popular input governs their evolution very strongly.
In practice, achieving a Union is toward certain ends. One of them is a strong collective defense. I have already sketched out how I think that might work, and noted that for various practical reasons, Swedish seems likely to be adopted as the standard form of command, in all cases where units of different nationality are communicating with each other. Thus all of Scandinavia's service members will be trained in Swedish to some degree.
Meanwhile, on many levels, the Union ought to encourage various kinds of intercourse between citizens on many levels. Corporations that were based in one nation or the other OTL will be encouraged to branch out with offices and plants and stores and so forth in the other nations, so we'd have managers and workforce cadres shuttling back and forth.
Media--radio, eventually TV--seem likely to remain in national control, but as consumers expressing effective demand, a certain cosmopolitan mentality will want productions of other member nations to air in their "markets." Sweden is nearly half the population of a three kingdom Union, and Iceland hardly makes a difference in this. But Copenhagen I believe would have a certain cultural appeal to Swedish audiences too, and some Swedes and Danes might be much taken with stories set in Norway.
I expect mass education to be advanced by the Union, with more opportunity for young Union citizens to go to some university or another, or to other forms of higher education. Opportunity might beckon for the young of one nation to relocate to another.
A pan-Scandinavian culture thus seems likely to rise, in which each nation, and indeed regions within nations, retain some sharp distinctiveness, but also shared commonality. This will tend to foster a sort of pidgin-creole "Skandish" commonly intelligible to many, with hip and trendy adoption of other language terms and grammar just for the style of it or forming hip in-group jargons to confuse the squares. This is after all the 1950s and '60s coming--especially if SU is in NATO and we have US bases here and there, there will be an invasion of rock and roll! Presumably ABBA had some such foundations OTL, we might, with NATO membership, have many such Scandinavian groups, and one that is popular in one nation seems likely to be wanted to tour the others.
For many reasons then, I expect the overall trend to be that on paper, in formal education, legal documents, and among certain cultural chauvinists, the several languages will remain sharply defined as separate, especially by any fussy official arbiters of proper language...but meanwhile a general Skandish lingua franca mixing and matching both diverse Scandinavian locutions and indiscriminately borrowing English (both Yankee and British) and to some extent French and German and who knows, maybe Russian (just to annoy the squares, you know, man?) and God knows what else. The more successful the Union is, the more this general argot seems likely to evolve.
In order to get Iceland to sign up, you'll need to balance federal/provincial powers though; no way will they sign up to anything which implies sacrificing control of sea/fishing at the very least, considering the dependence of the Icelandic economy on that sector. Likewise on energy, environmental and industrial powers considering the requirement for Iceland to be able to modernise it's economy and diversify at least slightly from fishing.
Well, certainly with fair apportionment by population, Iceland will be ludicrously weak in the Ting, having the smallest token of representation there. But against that, Icelanders will have more influence among fellow Scandinavians than they would in moving American decisionmakers with their own high handed notions; if Iceland does not join, they are pretty much on their own dealing with the Yankees. Also, a negotiated quid pro quo for joining and thus giving the Union far flung power to link up to their distant but weakly held holding in Greenland, would be ample pork in Union funding; small diversions from the three kingdoms will add up to handsome sums per Icelander capita!
Meanwhile the constitutional arrangement involves a conference of national governments as well as the collective popular vote Ting, and I think a council of heads of state (kings, and the Icelander President) is needed too. With these, Iceland can be quite sure to have its peculiar interests heard, noted and factored into consensus policies. Icelanders and Norwegians probably share similar interests in fishing for instance. Instead of dragging the Union into a head to head confrontation with the UK as OTL, perhaps the heavier weight of the entire Union will move the British to negotiate more reasonably and quietly, and the Union can get various conflicts ironed out to mutual benefit.
If Iceland wants to modernize--joining the Union is the best way to do it by far. Iceland is a prestige and strategic holding as far as the three kingdoms, especially Danes, see it--in return for that, they can reasonably expect a lot of money to be spent on Iceland, building up her ports, basing substantial Union (that is, nominally Norwegian and visiting Swedish and Danish flagged warships, but also a subsidized token Icelandic bunch of capital ships and small warcraft over and above Iceland's reasonable small coast guard fleet) fleet elements and air force assets based there, subsidized support for the Icelandic educational system elevating its best schools to world class university level. With NATO membership of the Union they also get the American and other member service bases there too.
I don't see any downside to Iceland joining. I can see that Iceland's politics and culture are out of step, that they'd worry about being de facto reabsorbed under Danish control again, as possible points needing negotiation.
The main variable about Iceland joining is US attitude. If the Union seems liable to stand aloof from NATO, Yankee policy makers will fear losing control of the Atlantic sea lanes and logistic problems reinforcing West Europe, and hang on to Iceland. Legally we can't do that of course, but I suppose there would be lots of informal channels to pressure and beguile Icelander voters and officials to resist the Union on whatever pretexts seem best to them. But if the Union is going to join NATO, integrating Iceland into a larger NATO partner, with the prior understanding that the USA shall be able to count on Iceland as a logistic and strategic base as well as added aid from the Union in the North Atlantic sea control mission, then Uncle Sam will instead want to influence the Icelanders to favor the Union.
Perhaps Yankee wishes will not be decisive, but I think it is fair to say that in the later 1940s, the USA had a lot of moral capital and was respected as a natural leader of the Western anti-Soviet alliance, and so I don't see it so much as strongarming, as a matter of which way the wind blows.
Union policy on NATO then is decisive here as in so many other issues.
FWIW I think the Scandinavian Union would in fact join NATO as a charter member.
