From what I’ve read, Putin would like nothing more than to drive a wedge between western allies. He’s never forgotten nor forgiven us for breaking up the Soviet Union. Likewise, he'd like nothing more than to serve some revenge and break up the western alliance.
Trump and the republicans are doing just that.
It's a lot more complicated than that.
Thinking of adversaries as motivated by pettiness only is not a particularly good way to view the world. Russians, in general, also don't think that the United States is responsible for "breaking up the Soviet Union." Many blame Gorbachev and Yeltsin, who generally have the worst retrospective approval ratings of any Russian leaders after the 1917 revolution.