I've been wondering what the exam will entail and I think there may be a student or two in the exam room.
Going to a teaching hospital is a very different experience. You have to totally change your expectations and just give yourself over to the experience. It's way more than a student or two in the exam room.
I go to LSU for specialist care pretty often, and it sometimes drives me crazy. I've also gone to private-practice specialists, and it's a radically different experience. When my beloved vet ophthalmologist left private practice to join the vet school faculty, I followed her, but I need 10x more patience on the visits now. She's as good as she ever was, but I have to brace myself to put up with all the vet students, interns, and residents.... when I really just want to see her.
First, we expect to have a third-year vet student (or pair of them) doing the intake interview in the exam room (what a vet tech would do elsewhere). They're always awkward and ask the same thing multiple ways. If they try to look at the dog, they often have no idea how to handle it. The dog will sense their apprehension too, so you have to manage that. They sometimes ask nonsense questions, and I have to ask them to try to rephrase when they garble what they mean to ask --they're learning how to talk to clients. Try to be patient, as every vet went through this phase of learning.
Next you'll likely talk to an ortho/surgery resident. The resident is already a DVM, but they're in the program to become boarded specialist -- it's VERY hard to get into those residency programs, so they were probably at the top of their vet school class. However, they're pretty inexperienced. They're working under the oversight of a faculty member (or several of them), learning specialty field over a two or three year period by actually handling cases under supervision. When the resident is at the end of the residency, they're almost ready to go out on their own and know A LOT; at the start of the residency though they tend to be far less knowledgeable and I sometimes have to say, "Can you check on the answer to XYZ question for me?" Then they run back and talk to their professor, and come back into the exam room.
Do NOT expect to be able to work directly with the faculty member/specialist professor. That's just not how things usually work at teaching hospitals. They want the resident to handle the client interaction, as that's part of the learning process. The faculty stays in the back, supervising the whole thing. They're involved in the exam, and the surgery, and checking on everything being done -- but the resident is handling client interaction. It's been very rare for me to talk to the faculty member, and when it happens it's usually because a resident was new and I'm an, err, intense/unusually knowledgable client asking too many questions they couldn't handle, and they gave up with the running back and forth and brought out "the boss." I usually get to see my ophthalmologist only because she's known me for years, so she comes into the room for me -- and I schedule on the days when she's there, but it's still the resident who's doing the initial exam, and then she follows up with "yes, that's right, and here's something new that I want you notice..."
You probably won't be able to watch your dog's exam. They'll take your dog in the back --- there, the faculty member will be demonstrating the exam, and yes, probably letting students put hands on your dog, as they need to feel the joint resistance and clicking or whatever is going on. I don't think they'd allow the dog to go through unnecessary pain, though. It's not just the residents who will be involved in that -- there will likely be a group of vet students assigned to their ortho module that week who will be learning from your dog. This isn't optional. If you're not okay with it, they may suggest taking your dog elsewhere as it's basically existential for a vet teaching hospital.
The radiologist will also be doing the same thing with your images -- with lots of eyes on them.
The appointment takes a LONG time as your dog is a case they're using to teach -- I have learned to just drop the dog off and come back later, instead of sitting for a couple of hours.
If there's more than one thing going on, they'll have multiple specialists involved. You won't find a more collaborative environment for challenging cases -- it's why they're SO good. You get really great vet medicine being practiced, often with some of the best specialists in the region involved in the case. However, the client experience tends to not be as good as it would be at a private specialty practice, as you're there as a teaching case.
OTOH, if there's an overnight stay, they'll have a crew of students and residents on duty and lavish a lot of attention on the dog. Students will love on your dog. Mine really seems to like going there, so I know he's getting positive attention when he goes back there with them.
Try to re-set your expectations and just roll with it. I used to let myself get a bit aggravated by how long things take, having to deal with so many students, etc. but it helps to remember that you're there BECAUSE of the expertise in a teaching hospital...so you have to put up with the "teaching" part of that. If you can't make peace with it, you're better off at a private practice specialty clinic.