Petitioning court ordered legitimation?

So my husband has two children with his ex, six year old and a nine year old. We have a set of two year old twins together. He has been paying child support for nine years for both of them. His child support is court ordered by her, and comes directly out of his paycheck every two weeks. He pays eight hundred dollars a month total for both kids. Ok, here's the thing, for the last six and nine years his ex has jerked him around about him seeing the kids. She has been only letting him see them on her convenience, under her rules, etc. She is your typical baby-mamma drama type. In the state of Georgia you have to pay to get your children legitimized and than pay for visitation rights. Finally, after having enough of her control with the kids, he paid a lawyer 2 thousand, went to court, got split visitation and legitimation. He now has equal rights. Yeah!!!! This all happened a month ago. She has now paid a lawyer of her own to petition him having any rights to his children. It's not that she doesn't want him to see their kids, it's that she doesn't want him having any say-so or rights to them. Like I stated earlier, she has done everything in the book to only let them see him on her terms. Now, she's pissed because she can't control things anymore. Can someone please tell me what grounds the judge would grant sole custody to her after him just being granted split custody for him?? He has no criminal or petty record. He works full time, we have a house, and as I stated earlier, his child support comes right out of his check. Oh, and by the way, I have nothing to do with their relationship. I came from another state not knowing anything about her or him or any connections like coming between them. He had been broken up with her for two years when we met.