John, who is married and has a job, can't get the right kind of child care for his child. OP and wife have no problem with that, provide child care.
Rebecca, who is unwed, pregnant, and in high school needs help with future child care. OP and wife are not okay with that, try to talk her into adoption.
So it's acceptable to be negligent and not get the care your child needs as long as you're married and have a job in this family. If you have neither, you get nothing. Stop pretending this is about the kid, and not about Rebecca not being married.
Don't be surprised when you have zero access to grandchild in the future. You have made it extremely clear you want nothing to do with this child. You practically even removed yourselves from the list of Rebecca's family when you blurt out that you won't be helping her at all, after her saying she'd like her family involved in raising her son. Which, quite frankly, is how a normal family works. You HELP each other. Not just your negligent son because he follows your religious indoctrination.