A couple of things. We are only hearing your side of the story. Which doesn’t mean you aren’t completely right, but there might be things you are missing. Second, it IS important that your daughter has a relationship with her father, and it seems that, whatever his other faults, he is willing to have some sort of relationship with her.
All that being said — he has obviously delegated his new wife to be the “heavy” and to manage all interactions. Is he lazy or clueless or what?
You don’t need his money and even if you did, he’s not giving you any. $200 a month is nowhere near enough to help support a child.
I could totally understand you wanting to cut him out of your life and your daughter’s given how irritating he and his wife are, but I wonder if there might not be other options?
For example, would his parents, or at least his mother, be willing to intervene? Hopefully his mom wants a relationship with her grand-child and maybe she’d be willing to mediate. Could you tell him and his new wife that you will have grandma help enforce certain basic rules? Would she be willing to do that?
Would they be willing to go to family counseling? What if you made the a pre-condition of further visits?
Finally, maybe consider changing the parameters — instead of sending your child to her father, offer to give him time with her whenever he likes, but she stays with his mother or yours (in other words, supervised visits). I wouldn’t do anything this drastic unless their actions actually put your daughter in danger, but…
My thought is — it’s important for your daughter to have as much love as possible. Even if her father and his wife are dysfunctional, if they do love your daughter, then it’s worth some amount of aggravation to make sure she has that relationship. However, nothing wrong with trying to address the issues by having someone mediate and so on.