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Sam,
No offense to the women here, but, as a father, you are unlikely to get useful advice on this board. There is a (perhaps understandable) reflexive suspicion of men here.
I find that most posts here are simply emotional support rather than concrete advice and actions that would benefit your attempts to regain contact with your children.
I strongly suggest you look at the website www.dadsdivorce.com It is a community of fathers going through divorce.
I will warn you, however, those guys will play rough with you if they perceive that your interest is simply revenge on your wife or trying to get out of playing child support. 'The best interest of my kids' is the mantra over there and they will tell you that unless your wife is actually abusive to the kids, she should be in their lives. Even a deeply flawed mother or father is better than none at all.
They have little patience for fathers that don't take care of their kids or who simply want to whine about how unfair things are. Some of the advice is in the form of a 2 by 4 upside the head to man up and WORK on the problem.
If things are truly as you say in your post, and she is trying to leverage the ridiculous VAWA statues falsely, you will get a lot of support and very good (layman level) legal advice. You should have a good shot at 50/50 custody. You are unlikely to get more unless the mother is drastically and provably unfit, the court system has a strong female bias when it comes to custody.
You will also get advice on how to forestall her taking the kids out of the country without your permission. That is a real danger in a case such as yours. See www.justice.gov/criminal/ceos/ipk.html
If it comes out that "it's all about you" and the kids may actually be better off with your wife, they will tell you that very bluntly.
Fight for your kids,
Bill W.
ps. You should also be aware that if you do find your kids, you can simply pick them up. You are the father and in the absence of court orders, you have just as much right to them as the mother. I would also file for an immediate emergency order to return the children to the marital home (I hope you have a lawyer). If she is unable to prove abuse, your presence and stability in the home will work in your favor in the ensuing custody battle. She has made a big mistake in trying to play 'keep away' with the kids. Don't let it pass without taking advantage of it.