All three are used. "Push someone's button" means to "elicit a (strong) emotional response from someone," and it could be either good or bad depending on the context.
"Push someone's right button" means to "elicit a (strong) emotional response from someone" but is used strictly for a positive (good) response. For example, commenting on the various attractive physical attributes of a woman, a man may say "gosh, she's pushing all the right buttons for me!" (sorry for this sexist remark! :D )
"Push someone's wrong button" means just the opposite, in that you elicit a negative (bad) response. For example, you could say, "Don't mention the word 'nose,' in front of Cyrano - it will push his wrong button!"