Dear @Ulyanovsk ... opposite to @Onkle Willie I disagree to most of your comment as it begins already flawed :I'd assume said military dictatorship ends up looking a lot like what the Reichswehr tried to set up during the Kapp Putsch: a militaristic conservative/paternalistic dictatorship. I think returning the monarchy under some form might be on the cards but if I were a betting man I would say not (pretty discredited at that point and doesn't really do much to aid the political power of the ruling Conservatives). The DNVP would be reconstituted and be a coalition of right wing and reactionary political elements, likely continuing some of the anti-semitic laws of the NSDAP but not to such an extreme. The Communists, SDP, and other left wing factions will likely remain repressed in the new political order and political prisoners will not be released from the camps (that is, if they aren't outright just put against the wall considering the camp system may not be utilized by the new regime)..
Since the Nazis are removed for their failure to reoccupy the Rhineland, it's likely this new government does not pursue nearly as bold a foreign policy as Hitler but a steady remilitarization (if they can*) and trampling of Versailles statutes would probably continue through the next decade. A collective sigh of relief will be breathed by all the statesmen of Western Europe..
I strongly disagree with the idea that a "democracy would be restored" even in name only - the Weimar Republic was openly despised by the same coalition of conservatives and reactionaries we are now placing in control of Germany. I can't see them plausibly making any moves to restore even the façade of republicanism in Germany. In terms of administrative initiatives, the Gau system of the Nazis is probably scrapped and Germany reverts back to the pre-1934 divisions considering NSDAP power is no longer a factor. Along with that, we can probably look at the planned structure of the Kapp government for a vision of this new order. I think Nazi strictures on culture like the demolition of so called "degenerate art" might survive the coup d'etat, but it's anyone's guess.
The economic situation will certainly be a rut for the new government to have to handle - Germany was funding it's rearmament through essentially currency manipulation and operating deficit spending through an imaginary company (MEFO Bills), but without a general European war and German conquests to even the scales against the deficit then this system was gonna result in serious economic woes. I'm by no means an expert on it though, so someone with more familiarity with the early Nazi economic outlook can offer something on that. To me though, it doesn't look promising.
I can't see the Second World War breaking out in anything resembling IOTL, if at all. Somewhere down the line maybe due to the expansionist ambitions of Stalin once he felt confident enough in Soviet (and by extension, his own) power to engage in foreign adventurism. It all depends on how things go elsewhere in Europe, but one immediate ramification of the removal of the Nazis is the probable withdraw of Nazi aid to Franco during the Spanish Civil War. This might make things a tad easier for the Republicans, although Italy will likely still be fully engaged there. Speaking of Italy, maybe this removal of the fascists give some inspiration to certain circles of Italian conservatives...
The Reichswehr was neither instigator nor participant in the Kapp-Putsch.
It was the Freikorps of Ehrhardt only that supported or rather drove the then commanding General of the Group(Region)command 1 including Berlin Lüttwitz and with him the conspirational group around Kapp into the though hoped and worked for by the latter but nevertheless very much premature Putsch-action.
And the reason for the Marine-Brigarde Ehrhardt ? ... being frightened to be disbanded/dismissed into joblessness aka loosing their income.
The true 'master' of the Reichswehr then already - despite an SPD-Reichwehr-Minister Noske - von Seeckt in anticipation of the general strike the socialists declared kinda 'striked' by reporting himself on 'holiday' immediatly what he strongly recommended to every other commander too. Though - admitted - he also dis not 'offered' or allowed regular Reichswehr to counter the Putschists.
Only military that - more or less - "served" the Putschists were some Navy-stations due to uneducated v.Trotha offering his services to what he rendered now to be the goverment.
For a "revival" of the DNVP ... it was already a dead horse in january 1933 only used as an at the moment still somewhat sore appendix. Even before it declined rapidly due to lack of a proper party organisation which completly evaporated later in 1933. There were still - without a doubt - single personalities who earlier deemed themself connected to the former DNVP.
Similar to the DNVP - aka lacking some party-organisation to be called as such - were KVP(offspring of DNVP), CNVD(another DNVP offspring), LB(the 'Agrarians'), DVP, DStP(parts of former DDP), WP, remants of DDP, etc.. But their members occupied even in 1936 sometimes even importnat administrational posts, regional, provincal or even on 'Reichs'-level. They were first and foremost CIVIL SERVANTS and already during the Kaiser-Reich the same during Weimar only way behind party-politicians.
Therefore the 'interim goverment' most likely installed by possibly the Wehrmacht after removing Hitler and surely with him his cronies might kave an outlook like a 'coaltion' including also center party catholics (the center in contrary to the other HAD a diffentiated well organised party-apparatus since Bismarck-times) but will see itself only as an 'experts'-goverment as was the self-esteem of the several Brüning-administrations.
Very likely one of the first steps taken by this new goverment would be to renounce all of nazi-jurisdiction socially relevant ... like the laws regarding euthanasia (un-christian), regarding expulsion of civil servants (regardless subliminal antisemitism NOT the buisness of party-politics; this is the civil service' only own domain) and also the Nuremberg laws as arbitrary and therefore 'un-civil-service'-like but most importantly disrupting economy - domestical as well as foreign - much more than it helps it. Most likely they would simply completly scrapped. And thereby Germany would return to the 'normal' globally (including United Kingdom, the US, France, Russia, Poland, etc., etc., etc.) prevailing kind of antisemitism.
Dedicated communists, left-wing socialists very likely would be kept in 'prison' eventually prison-camps but under 'new management' until all their cases would be resolved by law. SPD-men - if still in Germany and not escaped to France or Czechoslovakia - would very likely be freed as their incarcerations were conducted without valid juridication; though very likely very strongly remined NOT come in the way/conflict with the now ruling interim goverment. The assumption that a conservative regime would 'simply shoot them ... shows only quite some deep caricaturing non-understanding of the these people. IMHO
The try to reoccupy the Rheinland - aside from breaking yet another stone out of the 'prison-wall' of Versailles despite being part of the non-Versailles treaty of Locarno - was very much asked for BY the Wehrmacht as they needed it as a recruiting pool for their (yet still by themself steered and 'speeded') rearmament program. Therefore they would still put this task atnhands of 'their' interims goverment. Depending on how the events unfold I could envisage the 'usual' (aka non-nazi) diplomats kind of striking a deal - though somewhat later - to enable recruits to be drafted but not garrisoned within the demilitarised region. Not at least due to "A collective sigh of relief will be breathed by all the statesmen of Western Europe."
Conscription and at least the breach of the military parts of Versailles the Wallies had already accepted for over a year now. There actually was no need to "trample" on Versailles-statutes. The ToV was alreayd dead paper only. Nevertheless; as being fully legal the new goverment would very likely continue to try to revert the other effects of the ToV by political means. ... as had every goverment of he Weimar Republik - regardless if SPD or conservativly lead- since its signature.
Ofc after the 'overthrow' of the Hitler-regime there would be at first an 'Interim Goverment' of already mentioned civil servants as an 'experts'-goverment. In many part even continuing as they continued from the Kaiser-Reich to the Weimar Republik to the Hitler-state.
It should be kept in mind, that the civil service that run the country did not 'whole-heartly' supported Hitler it simply did not hindered him. What it did i.e. in 1920 with the Kapp-Putschists brought down by simply being ignored. by almost every official institution as well officials in person.
However these civil servants - despite eventual sympathies for this or that party or faction - strongly rejected any kind of 'party'-parlametarism or democracy. Nevertheless they strongly felt and thereby well understood the need of some kind of 'legalisation' of their rule or better admisnistration of the country. They would need some kind of 'sovereign'. Even the monarchists never envisaged absolutarian rule of 17th/18th century manner and asked for kind of a parliament. Though ... how its members might be choosen would be very different from Weimar practises. In whatever reform they would eventually instal to the Reich it would try to exclude any possibility for the so much abhored 'party-buisness' of the Weimar time.
Very likely in a frist step the "Reichsstatthalter"-law would be canceld and the 'proper' administrationalstructures without the nazis reestablished. ... with the prussian provinces as well as the Länder and other administrative subdivisions reinstalled. It should not be forgotten :
the nazis NEVER dissolved the existing structures of the Weimar times and its constitutions of the Reichs as well as the member-states. They only 'superseeded' them and in 1936 this was stll a rather week affait wiht many of the former administrators still around.
In the middle run there likely might be a Reichs-reform along the lines of Hugo Preuß and the Luther-Bund (sry no english translation available, use ev. google translate) probably in some part 'adjusted' regarding military district.
As said above : whatever the nazis up to that point of time had done regarding social buisnesses - including art - would very likely be reverted. ... including their 'management' of art, architecture and other cultural matters.
In terms of economy :
Hjalmar Schacht at that point of time is still THE MISTER BIG in financial and economic terms. Also no 4-years plan and no acceleration of the 1935 agreed upon rearmament program. The acceleration of OTL was actually by most of the top brass heavily opposed as being much too much far too fast to produce reasonable results. At that time Schacht had already quite a number of measures in stock which would have reduced the foreign traded burdens, not ast least the less agressive rearmaent and therefore better steering of export to generate foreign capital.
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