What is the ruling regarding a wife's refusal to be with her husband who is unable to fulfill his marital duties due to old age and illness? Is the husband's رضا (satisfaction/contentment) a condition for the validity of her Hajj in this case? And what should the wife do to remove hardship from herself and her children?

A wife's obedience to her husband in matters of enjoyment is obligatory, and she risks being cursed if she refuses. As for going for Hajj, if it is an obligatory Hajj, the majority of scholars believe that his permission is not a condition, because Allah's right takes precedence, though the Shafi'is differed on this. If it is a supererogatory Hajj, then it is not permissible without his permission. To solve the problem, the sister is advised to: be gentle with her husband, be patient with him, try to create a suitable atmosphere, occupy his time with beneficial activities, encourage him to perform Hajj with her, and make frequent supplications.