Is the husband entitled to take his son from his wife after Khul' due to the deterioration of the marital relationship and his sexual deviance, and must she return the Mahr if she requests Khul'?

This man is bad due to his abandonment of prayer, commission of indecencies, and negligence towards his wife and child. It is permissible for the wife to take what suffices her and her child from his money without his knowledge. He must be advised and encouraged to fear Allah, and supplicated for guidance. If he does not repent, then divorce is the solution, and it can be through khul‘ (a divorce initiated by the wife in exchange for compensation). After separation, the wife has a greater right to the custody of her child, unless she remarries. The father has no right to custody as long as he remains in this state, due to the failure to meet the conditions for a custodian.