Is it permissible for the wife to seek divorce due to psychological harm resulting from the ill-treatment of her husband's family and the husband's silence regarding it, and is it permissible for her to sever ties with her husband's family permanently?

What you mentioned about your husband's family mistreating you is contrary to Islamic law. They must fear Allah and cease their actions, and your husband must stop them from doing so. You are not permitted to seek a divorce; rather, you should strive to solve the problem with patience, by returning evil with good, and by avoiding them. There is no harm in boycotting them if maintaining ties increases animosity, but without a complete abandonment. Therefore, maintain greetings and let only good come from you, for there is reward in that and preservation of your home.