What is the ruling regarding a husband divorcing his angry wife if he says to her, "You are divorced"? And is it permissible for him to live with her in the same apartment, and what should he do if family members intervene to reconcile them?

A wife is not permitted to seek a divorce unless there is a legitimate Shar'i (Islamic legal) reason, based on theith: "Any woman who asks her husband for divorce without any [valid] cause, the scent of Paradise will be forbidden to her." If a husband divorces his wife, the divorce is valid, even if he was angry, unless his anger caused him to lose his awareness. As for a divorced woman living with her husband, it is permissible during her 'iddah (waiting period) if the divorce is revocable (raj'i), but it is forbidden if the divorce is irrevocable (ba'in). The efforts of the family to reconcile them do not obligate the husband to take his wife back, but if he sees benefit in doing so, then it is better to accept the reconciliation and take her back, because reconciliation is better than separation in most cases.