Is it permissible for a man married to two women to take one of them (the one who does not have children) alone to the market to buy household necessities, or should the second wife's trips to the market be frequent due to her not having children to hinder her?

The wives should be keen to remain in their homes except out of necessity, in compliance with the words of Allah Almighty: "And remain in your houses," and the saying of the Prophet, peace and blessings be upon him: "This (is her place), then the back of the mats." They may go out for an urgent need. It is more gentle for the mother of the children to stay with her children, and she can be persuaded to do so. If one of them has a special need that no one else can fulfill for her, then she should be allowed to go out. If both wives agree, there is no harm in one of them going out; otherwise, justice must be observed between them in terms of service and other matters.