What is the ruling regarding a wife staying outside the marital home for a month in the house of her married female friend, while her friend's husband is present with them in the same apartment, knowing that she uncovers her hair in front of him, and he is not one of her mahrams? And is it permissible to file a complaint with the judiciary even though she is still under the husband's marital authority?

If the wife leaves and lives with her married friend without her husband's permission and without a legitimate reason, she is disobedient (عاصية) and rebellious (ناشز). The husband has the right to prevent her from doing so, either by himself or through her guardian or the judiciary. Recourse to the judiciary should only be sought when reconciliation is not possible. If the reason (for her leaving) stems from the husband, he must apologize.