Is it permissible for a husband to perform Hajj while he is unjust to his wife, and is it permissible for him to perform Hajj with one of his wives and not the other?

Allah legislated polygyny on condition of justice between wives in lodging, food, and housing. Whoever fears not being able to be just should limit himself to one wife. This husband who favors one wife and neglects the other has violated justice and left her like one suspended. He must fear Allah and be just. As for travel, it is not permissible for a husband to travel with one of his wives without the other, except by drawing lots or with her consent. If he does so, he is sinful, and she has the right to demand her due or to be patient. The sin of injustice does not invalidate the obligatory Hajj for a Muslim who is able to perform it.