cherrybim:
Your comment carries a tempting emotional twang, and I hope to restore a bot of logic to the discussion.
1. Both according to halacha and secular law, child support and visitation are completely exclusive of each other. Mothers denying visitation to deadbeat dads is illegal. Courts have been used for that many times. So have courts been used to go after the deadbeat dads, whose refusal to support their children is illegal.
2. As I have cautioned before (comments above), support groups need to have proper focus in order to be beneficial. My displeasure with existing support groups for divorced or separated women was obvious in my earlier comments. Why so bitter? Because I have observed way too many instances of these networks becoming wellsprings of advice that guide women to engage in combat. No, I do not have a single nice word for a deadbeat dad. But nor do I have any positive thought about the readiness to make false allegations just to take revenge. The support groups I know (not by direction of the group itself, but by the suffering and imperfect members) shower women with empowerment to fight.
If I knew that the support groups would keep their focus on the real issue that require support, I would encourage and endorse them. The experience is quite upsetting, and those I know are providing the community a terrible disservice.