Most Helpful Girl
I don't think you're anywhere near a controlling douche. You sound like a good person, but you're letting her walk all over you. Does she think this is a polyamorous relationship or something? She can't be your girlfriend and have a girlfriend of her own. She's cheated, which is an automatic reason to break up in my book, but you're nicer than me and tried to stay and work it out. Even then she was putting you second.
Honestly, you don't need this girl in your life. She's just going to continue to disrespect your boundaries. I know you're crazy about her, but she's not good for you and if she cared for you as much as you care for her then she never would've cheated. Stay broken-up, move on, and find someone better. Tell this girl it's over and stop responding to her. You'll be much happier.