Is it permissible for the wife to request a divorce in this abusive manner, and what is your advice to her?

It is required that spouses treat each other with kindness. Wives have rights similar to their duties, as is customary, and men have a degree over them. A wife insulting her husband and accusing him of indecency constitutes 'nushuz' (disobedience/rebellion). The treatment for 'nushuz' involves steps, and beating is not the first, and it has regulations. A wife is not permitted to request a divorce except for a legitimate Shariah reason. If she insists on it without a valid excuse, he has the right to refuse until she offers financial compensation to free herself. We advise both spouses to exercise wisdom and deliberation to avoid divorce, especially when children are involved. The husband should strive to remove the reasons for his wife's request for divorce, and the wife should fear her Lord and recognize her husband's position, for his guardianship is one of management, not domination.