What are the legitimate rights of a non-Egyptian Muslim divorced woman if she refuses to return to Egypt, given that their child lives with the father's family in Egypt and that the marriage lasted 12 years?

A woman resides where her husband resides, and she is not permitted to refuse to travel with him unless she stipulated before marriage that she would reside in her own home.

The default rule for child custody after a marital separation is that it belongs to the mother, unless there is a impediment.

If custody is with the father, he is not permitted to prevent the mother from visiting her son, nor to prevent the son from visiting his mother. However, he is not compelled to send the child to her.

In cases of dispute concerning custody matters, reference should be made to the Sharia judge.