I cheated, she left me, I want her back?

Alright so, I have been with my girlfriend for two years we have a daughter together. Things were a bit rough for a little while but nothing serious just some joking around about seeing other people this and that. Anyway I have never cheated on her before until two weeks ago I met a girl on a job site she asked to be friends so we exchanged numbers I have to admit I was attracted to her but never thought of actually hooking up with her.

So about two weeks ago I'm out with some friends at the local pub having a few drinks, she calls me and I told her to stop by she did and we end up going back to her place after. I wouldn't say I was too drunk but I had a few to many. We hooked up and I had been txting with her for the past two weeks she talked with me like I was her boyfriend and I went along with it.

the other night I was sleeping and my girlfriend came home went through my phone and found the txts and woke me up and confronted me about what she seen. at first I denied it all then she decided to call the girl and find out for herself so I had to tell her the truth so I told her everything.

She packed up most of her stuff and left me. I deserve this. but I have so many feelings for her its killing me to be away from her. and my daughter. I regret everything and I can honestly say I would never let this happen again. I've been in close contact with her she wants to forgive me but I broke her heart and I know it won't be easy for her to forgive me. she game me a hug and a kiss last night for the first time then it seemed like we were on the road to recovery. but then I talked to her this morning and she was pissed off as ever.

Could some one maybe shed some light on my situation. I have no idea why I even did this to her. she is an amazing girl and I can't give up on her. how do I get her back. show her I'm sorry and that I never want to let this happien again?
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She said she loved me and wants to give me a chance when I can prove that she can trust me again! If she takes me back I'm going to ask her to marry me, something I should have done a long time ago.
I cheated, she left me, I want her back?
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