My husband and I wondered if he can sign his rights over to his three kids outside the home? He has spent most of their life in prison and two of the kids have a new father fugure in their life. Their mother wants him to sign over the boys

Signing over his rights won't stop him from having to pay child support.
Are you planning on having children with this man? Is this what you would want him to do for your kids? Just food for thought. Maybe he could try a little harder to see his kids and you can be supportive of that instead?