it doesn't matter if he's talking to you, or one of your others, he should not be engageing in shouting matches with patients.

He should not be saying the kinds of things he's saying to you. it dosen't matter how long he's seen you, or how much you say he's put up with from you.

he's at work. this is his job. if he can't contain himself during your sessions to the point of telling you to leave, he shouldn't be doing this kind of work.
people with DID have "imcomplete personalities" along with more complete alters. sometimes

they're called "fragments" it's not odd. I have them too.

He shouldn't be doing things to upset you, or encourage further splitting.

Going on what you've said here, he's not good for you. He may not know what he's doing. A thing that some therapists don't want to admit.

You need someone with experience with trauma, and DID.

Not a knucklehead who argues with alters. nothing they say should faze him a bit. He should expect it.