Girlfriend wants to work things out but says she is still going to be going out without me?

My girlfriend and I have been on a break for a month and a half. I caught her talking to some other girl and she has feelings for this other person. My girlfriend told me a week ago that she wants to work things out with me but says working things out means that she will not talk to this girl anymore. I have checked her cell phone records and I see texts that are sent back and forth from her and this girl. She has told me that she is going to stop talking to her for me because she wants to work things out with me and she has promised on us that she will not talk to this girl. I want to fight for her because I love her but it hurts so much. I have cheated on her in the past and she went through the same thing I’m going through so I don’t know what to do now. I get told to just do whats best for me so that I can be happy which is moving out and moving on then I get told that all my girlfriend wants is for me to show her that I love her and that’s what I’ve been doing. Please help what do you think I should do?