Is it permissible for a woman to seek a Khul’ (divorce at the instance of the wife) from her husband who cheats on her with his ex-wife and refuses to divorce her, especially since this has negatively affected her health and life?

If the husband is in this state, it is recommended for the wife to seek separation through divorce or khul', but she must first strive to reform him, advise him, and remind him of Allah the Almighty. If he does not mend his ways, then separation is recommended, and Allah may replace him with someone better, as He says: {But if they separate [by divorce], Allah will enrich each of them from His abundance.} As for the wicked things attributed to his ex-wife, they indicate her corruption and her efforts to cause discord among loved ones. She should be advised and made aware of the gravity of her actions, and that injustice may hasten its punishment in this world. If both spouses repent, there is no impediment to them reuniting in a lawful marriage.