Advice column answer:
Think about what it is you are looking for from this relationship. You can't change your girlfriend's past - it makes her the person she is today. If you love her for the person she is then that's all that matters.
Your children don't need to know her history, at least until they're adults, and it's certainly no concern of your ex-wife's.
Enjoy what you have together and talk about what you're both looking for in future. You have your girls but she may want to adopt children for instance. It's early days but you'll need to discuss it at some point.
Seems reasonable to me.