The former Kaiser Wilhelm II decided to throw his rather large amount of influence toward the communists because their social programs would help reduce the chance of total rebellion and anarchy which would destroy Germany. Banking on the former Kaiser's support, the communist party alliance gained a majority in the Reichstag and promptly took complete control of Germany.
ASB. This is taking Willy's congenial attitude towards the SPD in 1890 to insane levels. Legalizing a party is totally different from endorsing it for membership in the government; historically, the SPD
barely got into government during Willy's reign, when he actually had the power to do something, and one minister without portfolio is a far cry from controlling the country.
By the time he's deposed, he's not very popular, and his endorsement of the Commies wouldn't carry much weight, even if under some fit of insanity he made it. As for the talk of the "Communist Party alliance", at no point in its history was the KPD part of a coalition. It's only likely coalition partner, the USPD, split in 1920 (perhaps 1921?), half joining the KPD, half rejoining the SPD. The SPD hated the Communists and vice-versa, and co-operation between the KPD and any other party is ASB.
On Feburary 14, 1919 the communist president, Karl Liebknecht, proclaimed the formation of the one-party Kommunistische Republik von Deutschland (KRD), or Communist Republic of Germany.
Having control of the Reichstag doesn't mean a party controls the Presidency; the Weimar Republic had a directly-elected President not responsible to the Reichstag.
This outraged many nationalist parties, which consequently staged a civil war and recieved financing from several big businesses. In response, the Communists declared martial law and won the support of many people by promising jobs and healthcare for free. The business interests were powerful, though, and despite changing national opinion the conservative parties managed to hold their own until 1922, mainly through the support of the army. Much of the weakened German army supported the capitalists because it believed that Communism would lead to a disarmed Germany. German troops fired on German people, and in 1921 the army seemed close to a military coup.
No civil war in a twentieth century European country can proceed without support of at least part of the Army. If the "business interests" get the whole Army, the KRD isn't going to last a month; "many people" are not going to stop the Reichswehr, armed or not.
However, the communist parties finally managed to persuade the army that they would do everything in their power to make Germany great again, linking nationalism with communism, and ensured the army's neutrality.
With Liebknecht in power, and presumably in control of the Communist Party as well? You do realize this is the man who spent his whole life fighting militarism, who proclaimed during the war that "the main enemy is at home", and whose Reichstag career was spent proposing a bill for a people's militia that regularly failed? There's no way he'd make such a promise, no way he'd link nationalism with communism, and no way the army would trust him if he did. You'd need him assassinated, and even then the military leaders won't trust whatever Communist leader emerges from the power struggle (probably Paul Levi).
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Trotsky beat Stalin during this Civil War, and was hailed as a hero.
Trotsky and Stalin were on the same side in the Civil War...
Trotsky and the government embark on an industrialization program and collectivization of agriculture. Conflict breaks out with the peasants and the government is once again forced to compromise and allow some private enterprise (a return to the New Economic Program). Industry continues to be the economic priority.
Trotsky was a vociferius opponant of the NEP, and he was quite ruthless. He broke Kronstadt, he militarized labor, he reinstated disciplinary practices in the Red Army that had declined since the Revolution. He would be quite willing to put down peasant unrest (indeed, the OTL peasant unrest during the Civil War was put down pretty ruthlessly anyway).
Soviet government continues to be dominated by the Communist Party but power is exercised through the government organs. Lively debates continue within the party and on the Central Committee between the “Left Communists” led by Trotsky, Zinoviev and Kamenev and the “Right Communists” led by Bukharin and Tomsky.
Zinoviev was more centrist, Kamenev was on the right, and the Left Communists were more likely to include Miasnikov and Ossinsky than Kamenev and Zinoviev.
Please learn more about the history of the period.