Is it permissible to stipulate in a will that the children's custody remains with the current wife after the father's death, despite the presence of the mother who relinquished her custody, out of concern for the children's religious upbringing?

The purpose of custody (حضَانة) is to care for and raise children and to protect them from harm. The mother has the primary right to it. If she relinquishes her right, or marries, or commits immorality (فسقت), then the right transfers to the maternal grandmother, then to the father according to the majority of scholars. If the father dies, custody transfers to the next rightful guardian, and this is decided by the Sharia court after considering the condition of the relatives. The court's ruling resolves any dispute. It is not permissible for a husband to bequeath the custody of his children to his other wife. If the mother's immorality is proven, she is deprived of the right to custody.