Well, not too beat a dead horse, but here is roughly what I think what would happen after 1945.
The Freedom Party resistance movement would have one big final uprising somewhere in the defeated Confederacy, and maybe for a period ranging from a few days to a few weeks, they might even be able to establish a sort of reconstituted Confederate government, with a new self-declared President of the Confederate States of America. However, this new president of the CS wouldn't have been elected by the people he claims to represent, and in the end, the US military brutally crushes the rebellion by publicly executing anyone who it believes to have been a part of the new Confederate government.
By this time most people living in the defeated Confederacy, have come to realize that the US occupation cannot be overthrown, and each time a former Confederate official calls for rebellion, from the safety of their hidden bunker, it is the average citizen of the former Confederacy which suffers because of the rebellion, and not the shadowy figures lurking in redoubts across the land.
Although the attempt to reconstitute the Confederate government fails, it forces US officials to reconsider their approach to occupying the defeated Confederacy. A decision is reached by the Dewey administration that, under no circumstances can the Confederacy be allowed to regain any form of independence, and all other political and military concerns are declared secondary. Thus the decision is made to grant Canadian and Cuban independence, and to return Sonora and Chihuahua to Mexico for the purpose of freeing up troops for the occupation of the Confederacy.
Around this same time California Governor Earl Warren invites the President of Texas, Wright Patman to a semi-official summit in Los Angeles, California. Patman is dazzled by the freeways, swimming pools, and housing tracts of Southern California, and laments about the relatively low standard of living experienced by the people of Texas. A few months later Patman visits the White House, and a deal is struck to bring Texas back into the Union. The deal calls for the State of Houston to be reabsorbed by Texas, and for Texas to be able to keep its own small self-defense force nominally independent of the US military.
At first people notice the Marxist revolution playing out in Russia until it spills over into Alaska, and begins to threaten the newly independent nation of Canada. By the early 1950s the US finds itself having to permanently station troops along the border between Canada and Alaska. Raids across the border are carried out by both sides, and occasional flash point battles are not uncommon. Meanwhile, in Europe, a somewhat liberalized and democratized Germany continues to dominate the Continent through the creation of the European Confederation. Germany and the US (North American Treaty Organization) remain close allies throughout most of the rest of the twentieth century, has both blocks share concerns regarding the rise of Marxist-Trotskyism.
A cheap synthetic replacement for fossil fuels such as gasoline, diesel, and aviation fuel is developed in the mid-1950s, thus causing the price of crude oil to drop through the floor. A downside of this is that few automotive manufactures care about fuel economy or tail pipe emissions. Many western cities will spend the rest of the century cloaked in permanent layers of smog until atmospheric scrubbers come online during the 1990s.
The first manned moon landing occurs in 1966, the first personal computers are introduced in the mid 1970s, but the ability to post on the web is carefully controlled by the Federal Communications Agency.
An intense but short land based war breaks out in Japan home islands during the summer and fall of 1977. A US aircraft carrier is sunk as the US launches as a massive amphibious assault on Honshu. The US suffers heavy casualties, and superbombs are used in warfare for the first time since the 1940s. The war causes the Republicans to lose the White House to the Democrats in 1980. Also, the Japanese War is seen as the begging of the end of Marxist Troskyism, and by 1987, both the Russian and Japanese people have given up on the theory of government.
Towards the end of the century an alliance will begin to develop between Russia and the United States, as Europe and the People's Republic of China move close to one another.