Is it permissible for a wife to travel with her husband to study abroad without the permission of his other wife, especially since she is still living with her family and he has not provided her with accommodation?

A husband must be equitable among his wives in nightly lodging and should not travel with one of them except by drawing lots, based on the Hadith (definition) of Aisha (may Allah be pleased with her) that the Prophet (peace be upon him) would draw lots among his wives when he intended to travel. An exception to this is the wife with whom consummation has not occurred, as she is not entitled to division [of lodging] and her travel with the husband is not included in the lot-drawing. If the husband travels with one of his wives without drawing lots or without the consent of the others, he is sinful and must compensate the other wife for the duration of the journey and any stay within it. However, if the travel was by drawing lots or with consent, compensation is only due for the duration of the stay.