Should I give my ex another chance?

My girlfriend of over 5 years (and the mother of my 2 year old daughter) broke up with me on Nov 1st. We had been having some problems and after hardly talking for a week she said its best if we go our separate ways. Within a few days she was texting me how much she loved and missed me and wished she hadn't broke it off with me. So I told her we would talk it over when I came up to drop my daughter off at her moms 2 weeks later which is about an one 1/2 hr away from where I live (we agreed to equally share time with her). On the 9th she admitted she had been seeing and sleeping with this guy friend of hers and had started the day after we broke up. Now she says her and this guy are through and she wants to come back. I love her and had been paying on an engagement ring which was almost payed off (I got my $ back now). I had been planning to propose to her on Valentine's day and wanted it to be a surprise so I never mentioned anything to her about it. I want to giver her another chance but the fact that she started banging another guy within hours of our break up throws up a big red flag for me. I knew she would eventually find someone else I just didn't think it would be that fast. She left me for him and now wants me to just act like everything's OK. My brain tells me that I should say goodbye to her but my heart still has feelings for her. I feel like if I take her back something like this will happen again. On the other hand I feel somewhat obligated to try to work things out for my daughters sake and because I'm still in love with her. I need advice
Should I give my ex another chance?
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