Document everything all the time. All the promises, complains, make minutes from all calls and meetings and send them over with cc to boss or whoever. Answer accusations respectfully, but don't ignore them. Again, make sure both are documented. When the "bordeline abusive behavior" is actually accusation of something that is not true, address the accusation (but not necessary emotional tone).

Assholes will lie, willingly mis-remember, accuse you of their own mistakes and of consequences of their own decisions the moment first bug shows in production or something is not perfect. Be ready for that with documentation. Documentation does not make it easy and it will sux, but without it is even harder.

Let staff vent and talk about it, validate their feelings. But, make sure they are calm and respectful in their behavior toward client. Again, keep documentation.

Do not let abusiveness and rudeness dictate process. Do not do things that are irrational wrong or slow you down just because they were abusive or confrontational. You can do them as "client management" of course occasionally, but don't do them just because you are afraid of further abuse or rudeness. Again, document such things in a way that makes your objections very visible and makes it clear they insisted on it.