What is the ruling of Islamic law concerning a treacherous wife who confessed to committing an abomination and adultery, and how should her father's request for divorce be handled, along with the payment of the deferred dowry and custody of the son? Does custody fall away from a treacherous mother?

If a wife repents sincerely from immorality, then it is preferable to keep her and conceal her sin, and not divorce her, for one who repents from a sin is like one who has no sin. However, if she does not repent, then she should be divorced. The husband is permitted to refrain from divorcing her and to put pressure on her until she forfeits her dower or part of it. The wife has no right to custody of the child if her immorality is proven. In case of dispute over custody, the Shariah court will rule on the matter.