What is the Sharia ruling regarding the custody of children whose father has passed away, and their mother returned to her family and left them, then after a year she wants to take them with her, despite their attachment to their paternal family?

Custody of children is a right of the mother unless she remarries or there is an impediment, provided that she resides in the country of the minor's guardian, so that the guardian can see the child and supervise his upbringing. If the mother moves to another country, her custody right is forfeited and transfers to the female relatives next in line.