Is it permissible to legally seek to have the son live with his mother without the father's knowledge, given that the son resides in Egypt and the mother in Bahrain?

A woman married to a man who is a stranger to her children forfeits her right to custody, according to the saying of the Prophet, peace and blessings be upon him: "You have more right to him as long as you do not marry." She has no right to the custody of her son, and she is not permitted to move him from his country except with the father's consent and the consent of whoever has the right to custody, and on the condition that this is what is best for the child.