I think you are thinking too much about her past. Think about why she might not have been truthful with you at first. Do you really think it was to hurt you? Probably not. It's likely she just wanted you to accept her. She should have told you the truth, but look at your reaction now that she has told you. She's being truthful with you now and you're punishing her for it. Her past is not a good enough reason to suspect she's been unfaithful at all, that isn't fair.
As far as the relationship goes, it was a bad idea to get into a relationship with someone and let it continue knowing you weren't as devoted to it, but the children involved shouldn't suffer because you exercised bad judgment. I'm not sure if you have loved her at any point in the relationship, but it might be a wise decision to get some sort of counseling. Couples who were in love fall out of love all the time and right back in love after that. Relationships are work, they aren't perfect all the time. There's going to be times when you do not feel like you love each other. I suspect that there is something to the kind of person she is that you are attracted to, otherwise you wouldn't be sleeping with her.
As far as her reasons for her past, you really should stop and think before telling her she needs a better "excuse" for her behavior. You are not her, you don't know what her life experiences meant to her personally. Women who experience things like that are prone to be promiscuous, it's just a fact. It shouldn't say anything about whether or not she's worthy enough to be with you. And if it does, maybe you aren't worth her time.