...The only area in South America that have the necessary natural ressources for an early industrialization is South/Southeastern Brazil and unfortunatedly it simply didn't have the necessary social network to quickly industrialize (as Argentina could).
Could the latter factor be changed?
Supposing for instance during the period when the Spanish crown also ruled Portugal, that the Spanish authorities integrated Brazil into the Spanish administrative system, and encouraged Castilians to settle there. We might even postulate maybe that Portugal never regains independence from Spain and all Portugal's colonies are absorbed into the Spanish holdings permanently.
Could this set up a situation leading to a very broad and socially deep (including poorer mestizos and some Native peoples, as in Paraguay) revolutionary crisis in South America whereby a sufficiently broad region rises up against Spanish rule in a coordinated patriot movement, that unites a sufficiently resources-endowed region, perhaps with some post-revolutionary annexations?
Could the social gap between Spanish and Portuguese speaking peoples be bridged by common resentment and common struggle?
Say, the Portuguese speakers are divided on whether they wish to see a restoration of rule from Portugal or not, some agreeing with a great number of Spanish speakers (and Indian allies) that they'd sooner have a republic they control democratically, others being Luso-royalists--but the radical republicans are willing to work with the latter if it mobilizes enough popularity for success?
I have a rather wooly scenario in mind whereby a pretender to the Portuguese throne is offered the support of the South American revolutionaries, who will offer to enlist the Southern nation as part of his nominal domain, provided he agrees not to interfere in South American autonomy--they will be a dominion under his crown, but ruled by a continental parliament; they will first of all aid his bid for the throne in Lisbon by distracting the hell out of Spanish authority with their revolution, and upon gaining control of liberated territory divert some manpower and other resources to Portugal to assist in his taking power there, and post-crisis will pay a share of national taxes to Lisbon and otherwise aid Portuguese policy--building a local navy that will combine with Portuguese forces (assuming that in addition to continental autonomy the dominion gets a say in foreign policy set in Lisbon of course), vote armies to assist in Portuguese operations elsewhere, notably Africa while beefing up strength in outposts like Goa, Macao, and Timor and of course add greatly to his general glory. The revolution is successful. Maybe this Hispano-Portuguese speaking dominion remains a tail increasingly wagging the Portuguese dog forever (perhaps at a later date, the understanding that the Portuguese monarchs do not actually visit their South American domain is relaxed in return for Portugal, with the regions below the equator (South American, including Brazil, but also perhaps a Congo coming under de facto SA control, or a local largely African regime demanding and getting strong autonomy on similar terms to the South Americans) becoming increasingly decisive, and therefore acquiring a stronger stake in maintaining a strong comprehensive global Portuguese empire?
Or vice versa--the union of Spain and Portugal leads to a dynastic situation wherein a Portuguese dynasty gets control of the whole thing in Iberia, and imposes ATL policies that set up large swathes of the Empire of the Indies for patriotic revolution, again crossing linguistic lines, with a unified revolutionary movement combining support from both, again resulting in a strong South American multilingual, multicultural republic, or some other form of federation--a locally based strong and popular monarchy, maybe on Bonapartist lines?
I am too weak in understanding the details of Latin American politics, especially in this era, to be very decisive about what configurations of power might result in a long-standing union. It could be very authoritarian, it could be very clerical with the regional Catholic hierarchy coopted to support it, or anti-clerical with Jacobin sentiments leading to a culture war the radicals win, and perhaps fear of a conservative backlash helps keep the union together?
Again, which regions would have to be united to give the whole a good resource base, and how crucial is control of strategic resources to success? If the union has a friend in the USA, then anything they lack could be imported from the USA--barring determined British opposition, which might be a matter of treaties, punctuated with the occasional war in which the British are forced to make concessions, such as a policy of non-interference with trade.
I'd like to see a liberal power, whether a radical republic or perhaps a constitutional monarchy, under local or Iberian kingship nominally might not matter much. Such a regime would ban slavery and (to enable continental unity) have a decent policy regarding Native peoples who might thereby become bastions of the union. With such policies in place before abolition of slavery in the USA, one could anticipate antagonism, on an ideological level anyway--sheer distance probably protects them from direct clashes with the USA unless the union fronts on the Caribbean, as it might of course.
So which regions would need to be included, and what would it take to unite them? A strong Napoleonic emperor, if the basis of that sort of regime even exists? A widespread ideological radicalism that does not favor regional separatism?
It seems that including Brazilian claims is pretty important--if so, how much? Is just the southern portion of heavy early colonization, united to Argentina, Paraguay, Uruguay and Chile sufficient? Or must Bolivia and Peru be included? For that matter, is union across the Andes at all plausible? On the map the regions look contiguous but in terms of practical transport and communications the links between Atlantic and Pacific are weak, so either brute force or ideological unity are needed to bridge the gap, clearly.
On the Atlantic, are links between the southern cone including the Portuguese zone and "New Granada," the Caribbean region now including Colombia and Venezuela plausible? OTL they were separated by Amazonia and the coastal colonies of Britain, France and the Netherlands--annexing these would make for stormy geopolitics for the early union, whereas of course Amazonia is much more a barrier than a link. Should we stick with an Atlantic coast southern cone power--Argentina plus southern Brazil plus the small nations there, and leave incorporation of Chile, other Pacific regions, upper Amazonia, the three northwest European colonies, or the Caribbean "Spanish Main" to future aggrandizement? Or should we be focusing on New Granada, perhaps with extensions incorporating Peru or points south, including perhaps a swathe of Amazonia? A northern focus puts the region at immediate odds with both European Great Powers and the USA--but if it can weather these storms it might be strong indeed, and eventually engulf the whole continent by annexation.
I suppose to make any of these configurations plausible we need a POD well before the US revolution, and note that the OP premise assumes a USA of some kind exists in the former British colonies--it might not match OTL US borders or even have the same Constitution, although I think the OP presumes close correspondence with OTL on these matters.
Given a pool of sufficient resources, plausible means of transportation to pool them physically, and a political background making union plausible, the premise can be accepted, though obviously we'd want detailed answers to all these questions which would define the character of the union. Is it republican, liberal, democratic, populist, multi-racial in governance? Is it instead authoritarian, slave-holding, tied to European dynasties or in rivalry with them, or what?
Anyway, even if the center of power does lie on the Caribbean (which suggests to me it is as likely to expand north, taking control of islands and moving up Central America perhaps to OTL Mexican border, or even beyond it, conceivably annexing Mexico wholesale, or with Mexico being a founding member of the union even) then confrontation with the USA is still likely long delayed. Even if the region must wait until say the 1820s to form, if it holds widespread areas and its central powers are not too tied down forcing union on unwilling subjects, then it can command large armies and even acquire a strong navy if it can foster any industrialism, and by the time the USA confronts it face to face, its strength may be far stronger than say Spain in the late 1890s, even if it only has one or two generations of existence by the 1860s or '80s.
In that case, the USA is not going to regard it as a small power that can be overridden with a few Marines backing some corrupt local faction. The USA will treat it as a regional power, more respectfully than Mexico was treated.
We should recall of course that before the USA would be projecting power very far overseas in general, once a foothold on the Pacific is taken, presumably in Oregon, the USA now has a strong interest in South America based on freedom of passage around the southern tip to move ships back and forth between the oceans; the alternative being maintaining separate merchant and naval fleets and communicating between them overland in the narrow isthmuses of central America.
Thus a Southern Cone power would be of some interest to the USA, but mutual common interests would probably make relations friendly for the most part, even if the southern country is very liberal and has abolished slavery, while perhaps adhering strongly to Roman Catholicism--both would be obnoxious to some
Norteamericanos or other, and between them might alienate a majority, with Northerners having more of a problem with "Papism" and Southerners with abolitionism. But the distance is too great to fight about it whereas correct relations ease communications with the West coast. Later, even if this southern state adds to its "sins" monarchism and annexation of territories farther north, by the time Yankees (having presumably by then abolished slavery themselves) confront them more closely, their power would be formidable. If the southern power does not annex Panama and Nicaragua, I suppose even if relations are cool to hostile, the US course would be to get a canal built and control it--which might motivate the southern power to get its own canal built too. So--Yankee or British controlled canal in Nicaragua, southern controlled one in Panama.
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Suppose we hold to a lot of parallelism in defiance of mere butterflies, and that therefore sometime around 1914 a situation exists similar to OTL in Europe, with a Franco-British alliance including Russia confronting a Central power German-dominated alliance. In that case I see little reason to assume either the USA or the South American power, whatever its history and ideology, to be directly involved except as trade partners with Europe--and given the southern power is strong and independent, its situation would be very parallel the USA. Perhaps they too have gotten into the game of global imperialism, to a limited extent--I'd think the Southern power would be diverted toward Africa, perhaps with an in on extorting Portuguese colonies, so it controls Congo and/or Angola. They still might remain neutral in the early Great War, and as OTL the appeal of Entente versus CP is not symmetrical, because the British and French combined dominate the sea ways and would presumably have dominated both trade and capital investment in the south as well as in the USA. Britain in particular would see both in a similar light--lacking the bond of common language and culture with South America to be sure, but maybe aspects of SA culture are more appealing than some of Yankee. Aristocracy for instance; suppose the SA power has a working aristocracy along British lines, lordships for merit; intermarriages of poor noble houses in Britain with richer ones from SA might offset the Catholicsm of the Latins and seem more suitable than marriage to commoner Yankees. Not to the point the latter cease; the Yanks (most rich ones) are after all Protestant, English speaking, "whiter" for what that matters (a successful SA despotism or strongly aristocratic regime would probably have to be meritocratic so its nobles will be drawn on a more colorblind basis from the populace I'd think--or it would not be strong and independent if burdened with traditional Castilian racist hierarchal notions). Whatever--the bottom line is, such a south American regime, on whatever social basis, would like the USA be a place where big profits can be made with reasonable likelihood of success, although unlike colonial or third world investments the investing power cannot extort a guaranteed return--they must rely on the honesty, sound business practices, and integrity of local governmental bodies they cannot control of the big nation. But on the whole investment there would have been paying off, for British, French and other European investors; financial ties would exist and would probably be reinforced by family ones at high social levels as with the USA. To be strong and successful, the Latin American power would surely have considerable industrial development even if some resources must be imported.
Therefore in a Great War scenario parallel to OTL, the Entente, Britain in particular, would be favored by business interests in both American Continents* both fiscally and culturally, with the Germans having few to no ties save via immigrant populations--a strong South American state might draw in more immigration, diverting some from the USA, depending on cultural factors.
The big difference would be that Britain would not be courting the support of one transAtlantic power but two. Even if the southern power is substantially less strong than the USA, it would be worth a lot to get its support, whereas any German policy of trying to isolate and starve out Britain would be antagonistic to the southern nation's interests as to the USA, and liable to create incidents to mobilize support for the Entente.
Britain being able to solicit deals from either would not be in as poor a bargaining position as OTL. Entente powers would have bigger lines of credit, since they'd have it from South American investors as well as US ones, and could borrow more before needing a formal alliance on American terms. They would be drawing, for munitions and other war materials, on two pools of material resources instead of one. Conceivably the Entente might win the war without either American nation formally joining it, and have more lenient terms for paying back war debts. Or they might concentrate on drawing in whichever one is weaker first, presumably the SA power, and trading that nation having a privileged place at the peace talks for more lenient repayment terms; the South American power joining the Entente while the USA sits it out profitably enough means inviting a less overwhelming American partner in leaving the Europeans more in control post-war.
If we then continue the parallel "rinse and repeat" with a coming Great Depression, the question would be whether the Southern power would be likely to go Bolshevik or not (assuming ATL Russia did)--if we presume no it won't then the WWII situation again is different because again Britain can court both American nations again, while being somewhat richer to begin with. Would the southern nation be more likely to join the Axis than favor Britain? I think no, it would not be more likely to actually become fascist itself, though the question is open whether it has in fact been some sort of right-wing authoritarian power all along may be relevant. But in terms of self-interest regardless of ideology, it would not be rational to tie itself to the Nazis, at least not until Hitler appeared to be winning, and even then the regional interest would be to cooperate with the power most able to project power in its own region--that is, again, Britain. If it has not already gone Communist itself, then it will share US interest in checking both the Axis and the Soviet bloc. It is likely therefore to eventually support the Allies/United Nations side, and to have a very large say in the post-war order, probably being deemed a regional power dominating South America in Churchill's scheme of federated spheres of interest, which would carry them over to become a Security Council permanent member and veto power, having at least as strong a claim to it as either France or China. In the postwar setup, it will be in the Western sphere and at least as influential as Britain in western councils.
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*I am a Yank and was raised to think of them as separate, and ask this--if it is irrational to split the Americas at Panama, why is it sane to regard Africa as a different continent than Asia, let alone the division of Europe from Asia that is clearly a purely cultural, hardly geographic matter? If North and South America are one continent, surely then there are only 4 in the world--America, Antarctica, Australia and EurAfrAsia?
Viewed culturally rather than in terms of technical isolation, one might argue there are three Americas instead--South America south of the Orinoco ranges, North America with the USA on its southern border, and Central America/Caribbean between them. Then again Mexico has strong ties to the continent it is clearly a peninsula of so perhaps the border on land lies at the southern Mexican border, or even includes Central America down to say Costa Rica and Panama, these two being properly seen as Caribbean so there is no middle continent but an island region removing parts of the other two to it culturally?
Just dividing the two at Panama and the south Caribbean shore seems sensible enough to me.