Actually, she did try to get rid of him once, when she helped stage a coup on Olympus to oust him, and was one of the main conspirators, because she was tired of his shit. It didn't end well, Zeus came back after getting some aid, and punished everyone involved, except for Athena. Hera was forced to make a vow that she would never try something like this again, and swear fealty to him for eternity, essentially. Since then, she's bound twice over to not do jack shit against Zeus himself, so is forced to settle for his bastard children and love affairs in an attempt to soothe her rage.