<human>: Can you condense the text into a few key points?

I absolutely love my girlfriend and her family. That being said, she has depression and Bipolar. We met in college but she moved early on to be with her family when she couldn't manage school and her emotions. We had been dating for a bit so we decided to keep it long distance. She's always been loving and clinged to me. Unfortunately, we go 4 months at a time without seeing eachother except over skype.

For the past month shes been expressing doubt at my coming to be with her. She used to want it so much. We have talked extensively in the past about love, marriage, kids, and working together, (I'm going to be a doctor). The only problem we ever really had was she expressed disappointment in our sexual chemistry (I'm not very experienced) and never really was confident I could improve. 

Now after weeks of suspicion, she has come to me and told me she doesn't know what she wants. That she has feelings for another, a coworker, a waiter. They've been seeing eachother for 2 weeks under my nose.

She says she still loves me and want our future, to have babies, get married, etc. Now I have to make the move to her, to win her back, she promises me dates, but that we can't live together right away, that we have to start all over, completely. I know its dumb but I'm going to do it.

My question is, how do I confidently win her back when shes got someone else who she has better sexual chemistry with? She wants me but can't make a commitment? She can lie. I get it, I knew what I was signing up for when we started dating in regards to her emotional instability.

I have to move there, find work, pay rent, and expect to win her back from this dude. I know its unwise but I'm doing it. I just need to know how to go about it. We're talking later today but I have no idea what to say at this point.
<bot>: Gambling everything on a cheating girlfriend who wants me back but won't commit. Need advice on making it work, not why I shouldn't do it.