What are the rights of the wife and the fate of her daughters after divorce from a husband who engages in illicit relationships, is violent, and cruel, and is she entitled to intervene in their upbringing and care after the divorce?

If it is proven that the husband is engaged in an illicit relationship, he has committed a grave sin. The wife must advise him with wisdom. A husband striking his wife is not permissible except under specific Sharia guidelines. If the wife is harmed, she has the right to seek divorce after weighing the benefits of divorce against patience. Custody of the children belongs to the mother unless she remarries, then it transfers to whoever is most deserving among the relatives.