I think the Americans would have been wise to bomb the hell out of China and Russia.
In the 1950s the US still had some hopes that the CCP wouldn't survive too long, after all they still sponsored KMT destabilisation operations in this period.
Even with their edge in nuclear weapons, the US probably didn't have the capability to bomb China and the Soviet Union into submission. If nothing else, there was an issue of arsenal size vs. number and strength of targets. Those weapons would still have to be deployed from bombers, which the Soviets were capable of intercepting. Even if we assume the Soviets couldn't retaliate in kind against the US mainland, they probably could have retaliated against US bases in Europe etc. The aftermath would have seen the US without having achieved its objective, looking like a war-monger (after all, the USSR hadn't directly intervened in Korea) and with a bunch of very pissed off allies. Your scenario
might win the Cold War for the US, but it wouldn't win it much power in the aftermath.
Then take over.
The US, even with its allies, would not have had the numbers needed to control the Soviet Union and China. Nor would it have derived much advantage from doing so.
Basically this is another of your foolish fantasies.