My family was in a similar situation, my mums first husband (and father to my older siblings) ran off with another woman, he took all their money, sold all their furniture, etc. He had been violently abusive to my mother. No one heard from him for almost 20 years. He eventually contacted them when they were adults, only one of my siblings would have anything to do with him.
As for me, my dad died when I was 34 and my dads family made basically no effort to see me or keep in contact with me (even though we had a good relationship prior to his death). They acted like I didn't exist and that hurt so much.
What I'm getting at here is, yes she did an unforgivable thing. But it is worth hearing her out. I know it hurts you, but you should do it for your daughters sake. She deserves to have answers and she deserves a chance to know her mother if it comes to that.
Even knowing all the horrible, unforgivable things her dad did (like beating up my mother while she was full term, causing the baby to die), one of my siblings still needed to see him, to meet up with him, because it messed her up that he could just leave like that. Eventually she cut him off, but it was on her terms this time.
Her mother may not deserve a second chance, but your daughter does. No matter how good you've been at parenting her, knowing her mother abandoned her will mess her up and she is going to carry that around with her.
So I'd recommend hearing her out, getting answers to the questions you've been carrying around. If she wants to have a relationship with her daughter, then you could build up to that and make a judgement call at that time (but make it about what's best for your daughter in the long run, and not about your own personal feelings).
Also, your girlfriend probably shouldn't get a vote on this. Your ex, whom you loved very much and had a child with, reappears in your life... Of course your girlfriend doesn't want her back in your life. Few people would want their partners ex back in their life. But it's about your daughter, not your girlfriends feelings.