Can a mother move her child to texas from ohio without telling the father.?

My boyfriends ex moved to texas with his son while he was out of town for work. she will not let him talk to him or wont answer his calls. she wont give him her address to send money to support him. now she is trying to terminate his rights because she got married and wants her new hubby to be the father. my boyfriend is on the birth certificate but has never been to court for visitation. before she moved he was buying all the boys diapers milk clothes and any other needs. he provides his insurance and pays all his doctor bills currently. she went to texas for a couple months before to visit and he sent her multiple western unions to support the boy. now she is claiming he doesn't pay support but she wont' let him and he cant do anything about it because we don't have her address. can she have his parental rights terminated . she has sent him papers to voluntarily sign away his rights and her lawyer says if he don't sign them they are going to go after 3 years of child support and make him go to court in texas to try and keep his parental rights . the boy was born in ohio. all his family is here in ohio.
can they make him go to texas for court to fight for his rights. can they go after back support. was she legally allowed to move.
before she moved he was getting his son almost everyday even if it was only for a couple hours.
before she moved he was getting his son almost everyday even if it was only for a couple hours. he was only out of town for work for a week and he doesn't normally stay out of town with work.
he doesn't have reciepts but he has bank statements that show he sent western union. and he can prove he has insurance on him and has his sons dr bills to show she is using his insurance