What is the ruling of Islamic law regarding a wife who refuses to care for her sick mother-in-law, shows her hatred, and insists on staying at her family's home?

It is incumbent upon the wife to honor and serve her husband's mother due to the honor and love this brings from the husband, even if there is no legal religious obligation upon her to do so. A wife leaving without her husband's permission or a legitimate religious reason is forbidden (haram), and she must obey her husband by returning to his home. Inciting a woman against her husband is among the reprehensible acts. It is recommended that sensible individuals from the husband's family intervene to reconcile the wife and her father, and to appease the mother and strive to reconcile her with the wife.