Facetime isn't meant to substitute or replace visitation with your child. Virtual visitation

Virtual visitation

Virtual visitation is the use of electronic communication tools to provide contact between a parent and his or her children as part of a parenting plan or custody order. Virtual visitation includes many forms of communication, such as e-mail, instant messaging, and videoconferencing.

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is a supplement to seeing your child in person. You should be allowed to do both if the court grants the order.

Do I have to let my ex Facetime my child?

That's the short answer. Unless you have it in writing and it's signed that your ex must take your phone calls while they have your kids, they're not in any legal violation of any court order.

How often should a father call his child?

Unless there is a specific need, parents should not initiate a call or text to their children more than one time a day while they are in the other parent's custody. It is understandable to miss the child, but co-parenting requires respect for the child's time with the other parent.