What is the religious ruling regarding a wife who avoids serving her husband and his paralyzed father, claiming there is an unfounded impurity, and demands divorce if the husband does not move to another house?

A wife has the right to request independent lodging, and what is meant by independent lodging is a room with its amenities, such as a kitchen and a bathroom, not necessarily a completely separate house. If you provide her with an independent room with its own entrance and exit, separate from your father's apartment, then you have fulfilled her right. If the wife insists on her demand for complete separation or divorce, she is considered disobedient (nashiz), and you are not permitted to obey her in severing ties with your father.