Is it permissible for us to ask our father to divorce his wife judicially, because she is disobedient and abusive to him, despite his concern for the fate of their two children?

It is not permissible for a father to take his wife to court to compel her to divorce, but it is advisable to try to reconcile with her. If she persists in defiance (nushooz) and is not deterred, then he should divorce her while adhering to proper conduct and dignity in offering advice. It is not permissible for her family to assist her in her defiance, due to the words of Allah Almighty: "And do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty." So, they should fear Allah and assist the father in reforming his wife and urging her to obey him. Assistance from people of virtue can be sought for advice.