What is the ruling on a wife who does not care for her elderly father-in-law, nor for the cleanliness of his home and its facilities, and neglects her household responsibilities under the pretext that "this is not her home"?

A wife is not obligated to live with her husband's family or serve his father. However, doing so is an act of kindness and noble character. As for her service to her husband and cleaning her home, that is her duty according to what is customary, and her dereliction in it is a sin. She should be advised gently regarding serving her husband's elderly father, and reminded of the great reward associated with it if her intention is sincere. Assistance can also be sought from some righteous relatives.