Is it permissible for a wife to leave her marital home without her husband's knowledge and permission, and to travel long distances, under the pretext that her father is her guardian? And what is the religious ruling on that?

A wife's departure from her husband's house without his permission, and her refusal to return to his house without a valid reason, is not permissible and is considered nushuz (disobedience), which forfeits her right to maintenance if she is not pregnant. Obedience to the husband takes precedence over obedience to parents. Therefore, it is not permissible for the wife to leave her parents' house without her husband's permission, unless she knows he consents. If she refuses to return, some relatives or righteous people can be interceded to mediate and reconcile.