Can my Fiance sign over his rights if his Ex-Girlfriend is claiming Childsupport, but will not allow him to see his kids?

Its been six years since he has seen his two kids by his ex-girlfriend. She is demanding child support, but does not want her kids to have anything to do with him. He has always wanted to be in their lives. She has filled their heads with hatred towards him. He has put the thought into relinquishing rights. I am pulling two jobs, as I am a mother of another child of his as well. They took his license, so I also have to play taxi to drop kids off at school/daycare, take him to his job sites, and me to go to work. Mind you, my child is 1 1/2, I have no family here in Sioux Falls. They all live in St. Louis. My Fiance and I also share custody with his ex-wife with their child. He has contempt court on Tuesday, and both his ex-wife and I will be there to hopefully speak up. Would this be at all helpful? We are already suffering financially, because I am trying to work on my personal debt and our bills, and I am the one having to suffer through all this. Another topper, he has a felony and he is on parole. He is also having to pay those fees as well. I am beyond stressed out. I feel like I am doing everything I can to support MY family, but this is hovering over us like a sore thumb.