Is it permissible for the husband to divorce his wife who traveled with her mother without his permission or a mahram, after she left him due to family disputes and refused to communicate with him?

The wife's actions of insulting her husband and traveling without his permission and consent constitute a forbidden nushooz (disobedience) that incurs Allah's wrath and forfeits her right to maintenance and housing. If, in addition to that, she traveled without a mahram (unmarriageable kin), she committed another reprehensible act. Nevertheless, it is not advisable to rush into divorcing her. Instead, one should try to reconcile with her, be patient with her, frequently supplicate for her, and remind her of the fear of Allah and the husband's rights. If she persists in her nushooz, then there is no sin in divorcing her, and that might even be better, as divorce is permissible when there is a need for it due to a woman's bad character or her lack of chastity. It has been reported that three types of people supplicate to Allah, but their prayers are not answered, among them is a man who had a ill-tempered wife but did not divorce her.