How should a man deal with his wife whom he has divorced Islamically and who is committing adultery with another man, while she is still legally his wife and living in her family's house, a family that claims to be religious? And is he accountable for his daughter, who is living with her mother under legal custody?

It is not permissible to accuse a wife of adultery without proof. If adultery is proven by evidence, the implementation of the hudud (punishment) for adulterers is the responsibility of the ruler, not individuals. Regarding the custody of the daughter after the separation of the spouses, the general rule is that it belongs to the mother unless her immorality is proven. In that case, she has no right to custody according to the majority of scholars. Disputed custody issues are referred to the Sharia court for resolution. The mother's established custody does not prevent the father from seeing his daughter, caring for her, and disciplining her.