Most Helpful Girl
I'm kind of in a similar position. My boyfriend is rather an alcoholic and has been with so many girls he's lost count of how many. Most of his relationships never lasted before (an average of 2-3 months). However, we've been dating for four months, and I can tell he's really trying to commit to this one.
I study human relationship + psychology, and we learn that people just do not change easily. People can, however, make an attempt to change and/or restrain themselves from bad habits.
A negative is that she HAS cheated before. A positive is that she has admitted it and has committed to you for four months without sex. People who cheat usually either 1) never cheat again because of guilt, or 2) ends up cheating on multiple partners. Which one do you think she is? (Don't come up with excuses for her or the relationship - trust your gut!)
The key for relationships like this (or relationships in general) to work is both parties need to make an attempt to work it out. Yes, this will bother you to a degree, and being alert is NOT a bad thing. But you'r going to have to trust her by not acting possessive (this usually pushes the partner to cheat on you). If it bothers you, feel free to talk it out with her!!