Is it obligatory to divorce the adulterous wife who repented then returned to adultery years later, knowing that there are children, and fearing her destitution and the impact of that on the reputation of the daughters in Western countries, especially since she is remorseful and wishes to return?

If the wife repents sincerely and her truthfulness becomes apparent, there is no harm for the husband in keeping her, for repentance erases what came before it. However, if she does not repent, it is not appropriate to keep her, and the correct action is separation through divorce or khul'. Ibn Qudamah holds that divorce is recommended when a woman neglects her duties towards God or is unchaste, and it may even be obligatory. Divorce is not always evil; it can sometimes be good for both spouses, as Allah says: "But if they separate, Allah will enrich each of them from His abundance."