you give the us waaaaay too much credit. the us didn't split the ussr from china, the ussr did. de-stalinization pursued by khrushchev caused the extremely ideological purity obsessed maoists to denounce the ussrs flavor of communism in the late 1950s, and relations only worsened into the 1970s. nixon did take advantage of the split, but the us wasn't the causative.
United States