What happened to a father's rights?

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I have wondered about this for sometime now. Most likely because of what my Cousin is going through with his daughter and the mother of his daughter. He is fighting so hard to be a part of her his daughter's life. The marriage ended badley when he found out she cheated on him after he came back from his tour in Iraq. He is paying his child support and trying to give money for other things that his daughter needs as well. He has comprimised on the mother a lot. They have went to court over visitation so many times. He is also trying to fight to have his daughter have his last name because the mother gave her her last name. The mother has tried to control every aspect of the custody situation. She is even tring to get $600 plus a month now after it was agreed to pay $450. Granted she wont get it but she is trying anyway. They have done mediation but the mother went against the mediation agreement. Her own lawyer even quit on her. The last time they were in court she told my cousin she was going to do everything she can to make his life hell. She will most likely try! All because she has the one thing he loves more than anything. His daughter! You think she would be happy her child has a daughter who's father wants to be in her life and take responsibility. We all know that their are some dad's who are deadbeats and the mothers get no support of any kind from them. Instead my Cousin's ex uses the child like a weapon to hurt him any way she can. Do fathers have any rights?