What is the ruling on divorce, alimony, and custody for a disobedient wife who neglects her child and husband, refuses to obey him, and does not adhere to the regulations of Sharia, knowing that the husband has reduced her expenses after despairing of her rectification?

The wife has combined disobedience to Allah with dereliction of duty towards her husband and son. Her abandonment of prayer is the greatest sin, and attention should first be given to her rectification regarding prayer. If she repents, then praise be to Allah; otherwise, it is preferable to divorce her. Her actions are considered 'nushuz' (rebellion), for which the husband has the right to discipline her Islamically. The maintenance of a rebellious wife is forfeited, unless she is pregnant. 'Nushuz' does not negate custody unless she is deemed untrustworthy with the child, and the determination of her fitness for custody rests with the judiciary. Custody belongs to both parents as long as the marital relationship exists. The mother has a greater right to her child after separation, as long as she does not remarry. Divorce is permissible, especially if there is a need for it, and it is recommended to divorce a woman of bad character.