I feel there is more to this story. It's not uncommon for one parent calling and disrupting the time the other parent have with the child. Don't call unless it is necessary or make a deal that both of you can call to say goodnight. It can be disruptive for the child when they try to get used to the other home.
Not without the approval of the courts.
How often is the father awarded custody of the child over the mother in North Carolina?
the father gets the custody of the child if the mother dies
Take it to court.
The mother. If she dies, her parents get custody.
Father must petition for custody and court will weigh what situation is best for the child
He can still gain custody as the presumptive father.
A child does not need to be abandoned by their mother for a father to be awarded full custody. If the father can demonstrate before a judge that the mother is unfit to parent, the judge can award him full custody of the child.
The mother. The father have to petition the court for custody.
It is very rare that a Mother wants to give full custody of a child to the Father. To this all a Mother would have to do is choose to sign and give up her rights to the child in court.
I think it depends on how long the mother will be incarcerated for. There might be a hearing giving the father temporary custody. But if the father ever tries to get full physical custody of the child in the future, it might not be good for the mother. However, she can never be refused visitation.
Not if the person has a court ordered custody agreement. If no visitation/custody order is in place, it is at the discretion of the person who has custody of the child.