Do the husband's family have the right to custody of the daughter from her mother, knowing that the mother has not fallen short in raising the daughter, and the father is alive, and she is still married to him?

The custody of the daughter is a right of her parents as long as the marital relationship between them is ongoing. The father being a captive does not annul her mother's custody of her, nor does it entitle his family to claim her. Everyone must fear Allah concerning the daughter, and she should receive care, attention, and affection from all.