Is a husband obligated to divorce his wife if she cheated on him, given the presence of children and the threat to her life from her family? And is it permissible for him to kill the adulterer who destroyed his life?

If the wife's communication with a non-mahram man is proven, it is a disgraceful behavior and a grave offense. A righteous wife safeguards her husband in his absence, in herself and his wealth. It is not mandatory to divorce her; rather, he should advise her, remind her of Allah, and strive to educate her. If she becomes upright, he should keep her. If she persists, then separation is better. Divorce is recommended when the wife neglects Allah's rights or is unchaste.

The wife has no right to custody of the children if she does not repent, because immorality negates custody. Custody then transfers to the next deserving person after the mother.

Strive to raise the children. If you divorce her, do not mention the real reason for the divorce to her family to protect her from their evil, but rather say that you two were not compatible.

It is not permissible to accuse anyone of adultery without clear proof, and it is forbidden to kill this man, for the blood of a Muslim is sacred. The implementation of Sharia punishments belongs to the ruler, not to the general populace.