The only reason the US and Britain were allies with the Soviet Union and Josef Stalin was because they shared a common enemy: Germany. They never liked each other, never trusted each other, and even while they fought on the same side, they were conspiring and positioning themselves for a struggle with the Soviets and vice versa before the war was even over. It was an alliance of convenience.
Stalin did not trust either FDR or Churchill, because he thought they were stalling on invading France to open a second front, trying to bleed the Russian Army by not helping as much as they could. Actually, there is some evidence to suggest that he might have been right.
FDR and Churchill were great friends, but Churchill looked at the world like an imperialist, while FDR just didn't think that way. So Churchill thought him naive, while FDR thought Churchill too opportunistic.
A great book about this was just released. It's called Citizens of London.