What is the ruling on a wife's refusal to adorn herself and wear perfume, her refusal to leave the house, and her abstention from food, out of grief for the death of her brother, and what should the husband do about it?

What you have mentioned about your wife's excessive display of grief, her refusal to eat, drink, or adorn herself, is a form of forbidden wailing (niyāḥah), which the Prophet, peace and blessings be upon him, considered an act of pre-Islamic ignorance (Jahiliyyah), and he warned its perpetrator of severe punishment. This is based on his saying, peace and blessings be upon him: "The wailing woman, if she does not repent before her death, will be raised on the Day of Resurrection wearing a garment of tar and a shield of scabs." Her statement that she will continue in this state until the completion of the waiting period (iddah) of her deceased brother-in-law's wife contradicts the Prophet's saying, peace and blessings be upon him: "A woman should not mourn over a deceased person for more than three days, except for her husband, for four months and ten days."