Are the wife's actions—leaving the home twice, refusing to change, and insisting on her opinion—considered nushuz, and would the husband be unjust if he divorces her or marries another woman while still married to her?

Marital life must be built upon adherence to the Quran and Sunnah (definition), and the wife must obey her husband in what is right, as Allah Almighty stated: ﴿So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard.﴾ Sheikh Al-Islam Ibn Taymiyyah interpreted "qanitat" (devoutly obedient) as women who are obedient to Allah and their husbands in all matters. As stated in the prophetic tradition, a woman who prays, fasts, guards her chastity, and obeys her husband will enter Paradise through any gate she wishes.

It is not permissible for the wife to leave her husband's house except with his permission. If she abandons her obedience, she becomes disobedient (nashiz). The husband is permitted to admonish her, then to abandon her in bed, then to strike her with a non-injurious blow if admonition and abandonment do not work, as in His Almighty saying: ﴿But those [wives] from whom you fear disloyalty and ill-conduct, advise them; then forsake them in bed; and strike them. But if they obey you, seek no means against them. Indeed, Allah is ever Exalted and Grand.﴾ Disobedience (nushuz) includes her disobedience in bed or leaving the home without his permission, and is not limited to committing indecency.

If the woman persists in her disobedience and the aforementioned means do not reform her, the husband has the right to divorce her. He is not considered unjust to her; rather, she is the unjust one by abandoning her obedience to her husband.