Did Russia control everything that happened in its “member states” for lack of a better term, or did they have some form of limited government like the state system in America?
I link you to my previous answer to a related question on the matter .
As a summary, Russia did not control all the member states, there was a Russian government (of a Republic already federal in nature) and a Ukrainian government in apparent equality, and a government of the Soviet Union who was hierarchically superior to both. The trick here is that there was only one party, the Communist Party of the Soviet Union (CPSU), and since 1936 the "special status" of the CPSU was written into the Constitution. And the CPSU was centralist in ideology and structure, all the national Communist Parties depended on it, and Russia was the only republic without a National Communist Party. Thus, what actually happened is that to be on the leadership of Soviet Russia or the Soviet Union, one had to be in the leadership of the CPSU itself, that is one had to belong to the Secretariat, the Politburo, the Orgburo, the Central Control Commission or the Central Committee. And those were the bodies that controlled the whole party, that includes the members of the government of both the Union and all Soviet Republics or any other subordinate body. Therefore, while in theory the Chairman of the Ukrainian Council of People's Commissars (Radnarkom) was a leader independent from the Chairman of Russian Council of People's Commissars (Sovnarkom); in practice, as a member of the CPSU, he was subordinated to the decisions of the Politburo, one of whose members was probably the Chariman of Russian Sovnarkom.
Soviet politics are not simple to understand, because despite the apparent legality in their Constitution which clearly defined boundaries of the State and the Administration, the Parallel State which was the CPSU controlled every aspect of society, and it was organized loosely around personal cliques and controlled from top to bottom. That's why the General Secretary of the CPSU was the real leader of the Soviet Union, and not the Chairman of Sovnarkom or Prime Minister.