How do I deal with my sister's husband, who intended ill will toward my wife and the wives of my brothers, and who asked my wife for vile things, taking into account the Hadith of animosity and hatred?

If your sister's husband is behaving badly towards your wife and your brothers' wives, then he is a bad man, and what he is doing is serious. It is obligatory to advise him, remind him of Allah, and call him to repentance. If he does not repent, then boycotting him is permissible. The prohibition of boycotting for more than three nights is specific to worldly matters. Your wife and your brothers' wives must be wary of him and firm in dealing with him.