She cheated and I'm wondering what the heck I'm doing.

The girl I am dating was a friend for a good while before we started dating; I'll call her Lisa. We dated for two months, and then Lisa went on a trip for a month. She had already made the plans to go before we started dating, so off she went. Two friends went with her: one girl and one guy. During the trip the guy she went with told her he was in love with her, and, long story short, she cheated on me. Nothing physical, it didn’t last long, and it struck me as a very superficial quasi-romance. She’s immature and got caught up in a moment -- she realized that when “I’m in love” comes from a 22 year old from Paris it means squat.

I've already decided to give her a shot -- we haven't really been together long enough to develop a strong relationship. And, to be honest, she really has become an incredibly close friend. Here's the problem: I teach salsa lessons so I talk to a lot of girls, and she is a naturally jealous person. Right now there is one specific girl that is a problem -- let's call her Jill. I went on a couple dates with Jill before I started dating Lisa, but nothing happened -- I wasn't in to her, but Jill and I have become friends. Now Lisa (the girlfriend) -- post her cheating on me -- is telling me that I have to cut ties with Jill. To make matters worse Jill is very much into the salsa scene, and I see her all the time.

My girlfriend told me that she thinks I'm trying to one up her. Frankly, I think that's ridiculous. It feels like she's projecting her own capricious nature onto me -- she just doesn't believe that when I'm in a relationship I don't cheat. What do you all think: is it fair for the girl that cheated on me to ask me to give up a friend? I don’t feel like she has the right to ask me not to be Jill’s friend, because why should I have to give up a friend for someone I don’t trust. I mean, while I am giving my girlfriend another chance, if I cut ties with Jill (f), Lisa (gf) could very well screw up again and then I lose two friends. Perhaps I’m asking the wrong question. What would you do in my situation?
She cheated and I'm wondering what the heck I'm doing.
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