Is the wife's insistence on having a separate home for herself, given that she is suffering psychological harm from living with her mother-in-law, a sin, and is the husband sinful if he agrees to her request?

We ask Allah to help you be patient with your mother-in-law. We advise you to avoid despair, crying, and wishing for death. You are not obligated to live with your mother-in-law; you have the right to live in a separate residence. However, you should not request to move if your mother-in-law would be left alone and potentially harmed by it.