Which of the two is more entitled to a married man, in all respects: his mother or his wife? And is it permissible, Islamically, to leave a sick wife with her family so they can take care of her and cover the expenses of her treatment?

The rights of parents are great, and Allah has coupled His right with theirs, and the right of the mother is even greater. The rights of parents generally take precedence over the rights of the wife, except that the wife's maintenance takes precedence over the parents' maintenance, because her maintenance is in the nature of an exchange. The son must fulfill the rights of both the mother and the wife simultaneously.