It seems like you are the only one working to keep this relationship going and in that process your daughter is getting really hurt.
He is making it clear that he is going to cheat no matter what you do. If you can live with that-- then do, but don't take it out on your daughter -- that is your choice to be in the relationship; she has no choice but to be in a relationship with you... right?
Low self esteem leads to depression, anxiety, poor self image, and trouble with interpersonal relationships.
If you want to stay in the relationship, it sounds as though you already know that you need to find a way to not hurt your daughter in the process. You may want to consider counseling. That might help you to make a choie that will work for all of you.