If you are concerned that your dog is particularly anxious I would definitely raise it with your vet. I have had two different rescues that really didn’t cope with being inpatient and the vet was happy for us to stay with them until they were sedated if they ever needed to go in. They also tried to arrange it so we were first pick-up, as long as recovery was straightforward. Our vet explained that they would rather do everything they can to keep a dog calm and comfortable, than have to deal with stressed anxious dogs, which ultimately are harder to care for.
When one of mine had to be inpatient for a week at a specialist vet hospital, the lovely ICU nurses kept him with them at all times (he helped them with their rounds apparently 
) and that, alongside sedation when he had to be left, kept him much more calm and settled. He was a pretty extreme case though.
@vivainsomnia have you tried any of the OTC anxiety supplements for her around grooming appointments. The dog described above, who absolutely could not tolerate the vets as an inpatient, was able to go to our lovely boarding kennels, as we put him on Zylkene for a week before doing a tour, then an hour trial, then two hours, then a half day. We always put him on it a week before, just in case, but he loved going there, as we were able to essentially condition him to feeling calm and relaxed going there. We are just starting our current old boy on it now, as he’s developing some anxiety in certain situations in response to health issues. If Zylkene (made from natural milk proteins) doesn’t help, you could try a Tryptophan based supplement like Calmex or something like Dorwest’s Scullcap & Valerian compound and/or drops. (We used to use the latter for ferry trips for our dogs.)