What is the ruling on a husband's refusal for one of the daughters to serve her incapacitated mother, and what is the legitimate Shar'i solution for this problem, taking into consideration the children's health conditions and the mother's desire for her children to care for her?

Children must honor their mother and treat her kindly, and this includes serving and caring for her. This service is obligatory upon all children. They can either perform it themselves by taking turns, or they can provide a servant for her. If some children have an excuse that prevents them from serving her themselves, then they must hire a servant for her or share the cost of the servant with their siblings. If the mother does not accept the presence of a servant, then the children who are able to serve her must take turns doing so.