I have this same problem with my 3 youngest (Josh, Sassy, Sabrina) regardless of which cat in the house goes to the vet. Usually it's Josh & Sabrina that start most of the hissing which of course gets everyone else upset. So here's what I do no matter who goes to the vet.

I put Josh in the upstairs spare bedroom before I even bring the vet visiting kitty home. I usually have to leave Josh up there for 2 days before he's lonely enough to come out (yes I do go up and spend time with him so he's not actually alone the whole time).

Then I lock Sabrina in the bathroom before bringing the vet visiting cat home. She usually only has to stay in there for 5-7 hours, only once did she have to stay overnight in there.

Sassy usually does ok with the other cats so long as I don't let her sniff the vet visiting cat right away.

Once Sabrina gets to come out, I have to supervise her very closely, and if things go well she stays out, if not, back in the bathroom she goes for a few more hours.

Once Josh gets let out, same thing. If I let him out too early he gets Sabrina going, then they both get Sassy going and I'm back at square one again. I also have to make sure to feed the 3 separately and further apart for a couple days (normally they all 3 eat out of the same bowl).

And yes, I have to go through this EVERY time a kitty goes to the vet, no matter if it's one of these 3 or someone else that goes. Needless to say any trip to the vet results in a few days of kitty upheaval in the house. lol

Good luck with your kitties.