If a mother recieving child support refuses to let the father be around the child?

My brother has been paying child support for 4 years, the mother of the child refuses to let the child know who it’s father is. My brother has tried several times to be involved in the child’s life and the mother has only allowed to him to meet the child a few times (only being introduced as a friend). The mother has allowed the child to spend time with everyone else in my family and the child knows how we are all related to her, but has completely excluded my brother as being related to us.
It’s confusing but basically, the kid knows my mother is her grandma and that I am her aunt, but she doesn’t know how we are related to her father since she doesn’t know she has one. She’s only 4, so she hasn’t tried to connect the dots yet.
The mother is currently trying to take my brother back to court for more money because she somehow found out my brother got a slightly better job. My brother and his wife (of 1 year) recently had a baby, his wife is not working at the moment so my brother has been working a second job just to make ends meet.
The only reason the mother recieving child support refuses to acknowledge my brother as the 4 years father, is because my brother refused to be in a relationship with her and this has caused her to greatly dislike my brothers wife. Since the wedding, she has refused any and all attempts my brother has made to be in the child’s life.

I’m sorry this is probably confusing, it’s hard to explain the situation because its so messed up. I’m really just wondering if what she is doing is completely legal? Clearly she is being a bitch, but can she really continue to keep the child from its father for petty reasons while seeking more money from him?