How can I get visitation rights revoked ?

Her father moved to the East Coast when she was about 2 and has not tried to see her in 4 years. He refuses to pay child support (works under the table, won't file past years taxes which resulted in IRS audit, lied to employers about owing more than 6K in child support, child support enforcement finally revoked his drivers license because of unwillingness to pay). The father has a girlfriend that has a child who he says he is adopting (hopefully a smart judge will throw the request out). My childs father really only gets a job to support a girlfriend. He will not voluntarily pay child support, even though his last job paid $1100 a week. He states $336 a month is too much to pay in support, yet he lives in a state with very low cost of living and is adopting someone elses child??? My daughter has dental issues that come from her dads family (they have false teeth by 30) and I spend about $1500 a yr after insurance to fix her teeth...my other child has perfect teeth thankfully! Monthly her meds run $65, she sees a counselor weekly because of issues she has with her father leaving, daycare is 250 a month, and that isn't taking into consideration food, clothing, and basic necessities. Her father tried to tell me its my obligation to pay for her to travel alone to see him which I can't afford and am not going to allow him with her alone since he tried to kidnap her 4 years ago. I feel my daughter would be better off without him sporadically calling saying he will visit, telling her I'm mean, saying he is adopting a child, and threatening me. He can't afford to take me to court for not allowing her to visit alone but i'm thinking termination of visitation rights will actually help my daughter. This guy has mental issues and won't take meds for it, also was set to receive disability benefits from army and social security which would have paid child support but he didn't want to finish his appointments, and he's tried to kill his mother.