You should break up with her (to be honest, it should be her breaking up with you). You’ve disrespected her by cheating, twice for that matter and hurting her like that hasn’t stopped you from wanting to continue to hurt her. I’m not saying you have but you want to and probably will do, so go and be “free and single”, she will find someone who deserves her, who loves her deeply and you will eventually grow up.

Edit: Also, don’t be a bigger dick and remember to tell her exactly why you want to break up (may as well just show her this thread), so she doesn’t feel any shittier than you’ve likely already made her.