Must a wife inform her husband and seek his permission if she wishes to temporarily move to another town (her parents' home) during his absence?

The fundamental principle is that a woman should not leave her husband's house without his permission, unless it is out of necessity. However, if the husband is traveling and the wife has children, she may travel with her family without her husband's permission, unless he has forbidden her from traveling and moving around, in which case she must seek his permission. Ibn Uthaymeen also issued a fatwa stating that a woman's going out depends on her knowledge of her husband's stance: if she knows that he allows her to go out for a need, then it is permissible for her to do so; otherwise, it is not. And if the husband is absent, she may go out as long as he has not forbidden her.