Is the mahr (dowry) to be paid in installments, and is the wife's departure from the marital home due to the non-payment of the mahr considered nushuz (disobedience), and can the husband demand her return to the house of obedience in this situation?

The Mahr (dower) is a right of the wife that does not lapse except by her waiver, and its installment payment is permissible with the agreement of both parties. It is not permissible for the wife to leave her husband's house without his permission, except for a legitimate Shar'i (Islamic legal) excuse, otherwise, she would be considered defiant (nashiz). If the wife does not have a legitimate Shar'i reason to leave, she must return to her home; otherwise, the husband may refer her case to a judge. It is not permissible for a woman to seek divorce without a legitimate Shar'i reason, nor for her family to incite her to do so. If the wife dislikes her husband, she may seek a Khul' (dissolution of marriage initiated by the wife) in exchange for compensation she pays, and this compensation may be her waiver of the Mahr. The husband is not obliged to divorce his wife, but if the marital relationship deteriorates and reconciliation becomes impossible, then divorce is preferable.