I know this is 1mo old, but since it wasn't answered...
First of all, psychology and science have come to believe that cheating is in our genes! It is not an "excuse" but it does demonstrate that the tendency to either cheat or be loyal is a born trait. With anything born, it can be overcome but not easily. First of all, she would need to want to change and overcome it. Most people say they want to change when they really have no intentions to try.
My own opinion on this woman is that you should remain friends. If she really wants you, she will make an effort. You should not be going after her. She should get some form of therapy for her cheating behavior. It could be born or it could very well be nothing more than insecurity. Although it is upsetting to be cheated on, more people need to be aware that it is not an option for people but more of a behavior issue that either must be accepted or treated. If you don't mind having an "open relationship" than maybe marriage could be in your future with this girl, but if you can't except the idea of knowing those lips aren't just yours to kiss, you should look elsewhere. You have a long road ahead of you with this girl. Good luck! You'll need it.