No offence, the only thing that would make a woman give up her kids is plain stupidty. I know the pain is a killer. You have to ask yourself one thing is this the type of woman you want to be with forever?
My answer would be no but each to their own. She sounds ruthless and will stop at nothing to hurt you so my advice is get out and stay out. I have had a simlar problem (on a much smaller scale) but all the same and i would kill to be with her again but that may never happen so all you can do is prepare yourself for the future YOUR future.
Never look back keep looking foward and remember that you were once happy without her so then you can be happy again without her.
The pain will stop sometimes it can take a long time but use that time to heal and grow..
Have a good one and good luck to you.