Under Tennessee law an acknowledgment of paternity can be rescinded within sixty days. See Tennessee Code Sec. 24-7-113(c). After that, legal action is required. If your son was married to the mother, raised the child as his own and wants to maintain his paternity, he has a good chance of maintaining his parental rights through the divorce case.
Mom's child from a prior marriage, though? He's unlikely to get access without the mother's (or that child's father's) consent.

