Child is going to be 16. His father is the non custodial parent and right now has standard visitation but due to his being on call 24/7 and the relationship between the 2 of them does not want visitation can he be made to have visitation. He has tried living with us 3 times and always ends up in trouble and wants to go back to his mom.

Giving up parental right means what in the State of Texas?
Is the non custodial parent still responsible to carry insurance, pay child support, etc.

Your post is a bit confusing... "and the relationship between the 2 of them does not want visitation can he be made to have visitation."... can who be made to have visitation?

Who is "us" that he has tried living with? Are you his father?

Try to explain a bit more for us please. Thanks.

And the only way for a parent to "give up" their parental rights is if there is another person (step parent) willing to adopt and accept the responsibility of that child.