Parenting time has to be done through the courts or else it means nothing. Notetizing an agreement doesn't matter legally in the matter of who has custody and visitation with the baby. It has to be signed by a judge in family court. Custody is important you and your son can have that baby whisked away from both of you unless the court says otherwise. I'd do it that way. It's the only legal way.
Your sons prison time may cause a court to require supervised visitation. Not sure about that.
Her mental illness won't matter unless there are police reports....she has to be proven incompetent in court. But it's better to have some legal custody days/times, even supervised, than have ex girlfriend fly off to another coast with the baby. Without court, she can do anything and she isn't breaking any laws. Most custody awards address not taking the baby too far away from the other parent.
Can you tell that my own adult child has been in a custody battle? Trust me, it's easier to do it in court than to write it down and hope flighty mother of your grand abides rather than decides to leave the state without informing your family where she is going.
