This stuff is tough I know...my situation is similar to an extent.
In my opinion your husband does not need to play tug-of-war. He made a mistake in not educating himself on his rights before, and now understands what they are fully, yes? Forward movement. It sounds as if y'all are putting in place the necessary; child support. CSEA (child support enforcement agency as it is called here in OH)can be relatively flexible in what is 'back owed'. In your budget where possible, build in an extra payment to CSEA (not the ex) to catch up on what is behind. Next fully understand your rights (your hubby's rights specifically) and demand visitation and follow through with it religiously. The court's have already set in place what his rights are, and the longer he doesn't take advantage of them the stronger her (the ex) case becomes. The only point that this would become a tug-of-war is if she refuses visitation (which typically an officer present with you when you arrive to pick up the child can and does correct that problem) - If not, she is in violation of a court order and will have consequenses to suffer legally...OR she pays an attorney now and has to prove your husband unfit in order to take his rights away.
My husband struggles with choosing to 'play tug-of-war' or not and I am always quick to offer him the view that tug-of-war may be difficult now, and you may belive you saving your son some heartache, but I truly BELIEVE that choosing NOT to battle for your rights to be his father, his daddy that he wants is more damaging and harder to overcome once he is an adult....
Food for thought....
Best of luck!

I totally agree with Maia in everything she said. The only thing that I would add is that if your husband doesn't want to assert his visitation rights, when his daughter gets older, she will always think that he didn't care enough about her to fight for visitation.
My husband and his ex went through court battles for the first few years. When we moved to another state, we were able to change the jurisdiction of the court to the new state. This put a stop to his ex filing motion after motion because it was cheap for her to file. My stepdaughters then felt as though their mother didn't care anymore because she couldn't file for custody. We had to explain why she couldn't do it, because they were so upset. Child support has nothing to do with visitation. The court will not just take away his rights as a parent because he's behind on the payments, so he shouldn't let his ex talk him into it. Have him start asserting his rights to visitation when he's supposed to have it. This will show that he is not abandoning his daughter. I wish you the best.

It's a little more complicated than that. His ex-wife has aleady proven that she can have him arrested for charges that don't even exist. She had people lie to have him thrown in joail. He is worried that even once the legal battle is over, that the emotional battle will remain.

It's the emotional battle he doesn't want to put his daughter through. His mom used him as a pawn to get at his dad. He doesn't want his ex-wife to have that opportunity as she is far more manipulative and vindictive.

How do you battle someone that will litterally stop at nothing?

You're right, that is much more complicated. Did she just get him arrested, or did she get him convicted? I understand why he doesn't want his little girl used as a pawn, I don't think anyone in their right mind would want that, but does he want her thinking that he gave her up? Sorry for such harsh questions, but I think they have to be asked.

He has thought about that. HE wants to still be able to put money away for her and for her to know who he is. SHe petitioned for his rights, but we can do it on our terms where his daughter still knows he is out there. Also, when she is 18 we can give her access to her bank account and give her a chance to make a decision on her own.

She got him convicted. Small town where he parents have connections. They actually proved him innocent but worked a deal with him instead of letting him off the hook. It was a mess.

He is worried she can not only do the legal stuff all over again, but she is using it as grounds to try and have his rights revoked.

She's already been known to show up and take her daughter forcefully from being with my husband.

He doesn't want his daughter to be split in two. Since she has a step father already, my husband feels it may be better to not fight. At the same time he really doeasnt want to let he go. But he wants to do whats best for her. Determining that has been very difficult. He's not sure what he is going to do.

That sounds like really complicated stuff. It sounds like your husband has given it a lot of thought. The one thing that I would give you to think about - if these people are doing this to your husband just because they are "well connected," then they could be doing it to others for different reasons. Maybe you should contact someone at the State's Attorney's office to find out if anything can be done. This can be done anonymously. I just never thought that something like that can happen to someone in this country.