Is it permissible for a wife to cohabit with her addicted husband who swore to divorce her multiple times, the last of which was using the صيغ (formulations) of the Shafi'i, Maliki, and Hanafi schools of thought, given that they have three children together?

If the husband utters a clear, unequivocal divorce (talaq) that is not contingent on an event, then a single divorce occurs. However, if the husband frequently swears by divorce and then breaks his oath, he must distance himself from his wife, as she has become irrevocably divorced from him (baa'in). If the divorce is contingent on a specific matter, the majority of scholars hold that the divorce occurs. Shaykh al-Islam Ibn Taymiyyah, however, opines that the one who utters such a divorce is obligated to pay an expiation for a broken oath (kaffarat yameen) if he did not intend divorce. The matter should be referred to a Sharia court to examine the details of the divorce issued by the husband. If it is proven that the husband is an alcoholic and frequently swears by divorce, the wife has the right to seek a divorce.