play one side against the other
To manipulate two opposing sides of an argument, conflict, competition, etc., against one another for one's own benefit or advantage. My father and my uncle are engaged in a bitter business rivalry. If I can play one side against the other, I might be able to secure some sizeable investments for my own company. Janet really dislikes Mary and wants to date her boyfriend Mike, so she's been playing one side against the other to get them to break up.