Whether explicitly stated or not, the woman gets a lot of benefit of the doubt in custody cases. Make sure to lay all her closet skeletons out for the court to see, including any neglect or poor parenting issues. I assume she's the non-custodial parent because she can't be bothered with the kid.
Was there ever a support order? If she broke it, it's contempt. Oh, well, I'm sure your lawyers have looked at that. But, make sure to bring these things up. Never assume a lawyer will have knowledge of all papers you give them - you would be surprised how little they know about your "file."
Oh, I know some guys with rubber hoses over that way if you need one of *those* referrals.