Do you really want to be with her? Or are you staying because you feel she needs you and you kind of feel nostalgia/guilt/ a need to fix things and have them be as they should?
Does being with her (and the anxiety and problems that brings) make you really happy or do you reckon you could be happier somewhere else, with someone else? Are you staying for the kids? Kids prefer stability, whether parents are together or divorced, so long as things are peaceful and on good terms that is way better than shaky uncertainties and knowing someone is hurting.
Based on what I've experienced I say sometimes love really isn't enough. If a person treats you really badly and you can't truly be who you are with them or are controlled, manipulated and constantly limited by them, you just have to decide what you want and what you can handle. Can you be there as a friend? Can you not be there at all? (If she is a really toxic influence on your life). Do you WANT to be the person that you are with her?
Ultimately it's up to you. Based on the way you express yourself I suspect you know what you want to do already but are kind of wanting someone to tell you it is ok to do what you want.
PS: The reason she wants to be monogamous MAY be because she wants YOU to be faithful to HER.
In my own opinion: I would leave her. You have been there for her WAY too many times and she blatantly uses you, she seems to have no remorse and seems to treat you really badly, almost as a back-up plan (I'm sorry dude, that's really harsh, but it really seems that she has no concern for what you feel so long as you are there for her. )
You have rights and feelings too and need to live a life in which you do not feel that you are someone else's property instead of what you are probably feeling by this point: that none of your own desires, personality and priorities are allowed to matter the way hers do.
You don't need permission or approval to live your life, all you need is "I want this. I choose this." (Just be honest and decent with people, remember the golden rule.) Remember: life is not a law court. You don't need to give evidence and win the argument or justify anything to anyone. YOU have the power to make your own decisions.). Don't put up with someone who continues to lie and cheat. You deserve much better and it sounds like some women out there have noticed this and appreciate you for who you really are. Just never make the mistake of leaving your real friends for those who treat you as expendible. Don't do what she is doing.