Should the husband comply with the reconciliation efforts with his wife who left the marital home and sought divorce, or should he "change the threshold of the house"?

You have done well by marrying with this intention, but you have done wrong by hitting your wife in the face, and you must repent sincerely. Do not utterly despise your wife, for if you dislike one of her traits, you will find another pleasing trait in her, such as religiosity, beauty, and chastity. If she possesses good qualities and you perceive nothing but stubbornness and the like from her, then be patient with her and strive to rectify her. Avoid divorce as much as possible, unless its benefit outweighs its harm. A wife leaving the house without her husband's permission or a legitimate excuse is an act of defiance (nushooz), and covering the face is religiously obligatory when going out or in the presence of non-mahram men. It is not permissible for a mother to incite her daughter against her husband.