Being a certified vet tech and having been in the field for over 15 years I think I can speak with a bit of knowledge.
I have never heard of, or worked in, a practice that took the animals into the back for routine care (ie vaccines). Blood draws, anal glands (if that is the only thing they are coming in for), x-rays and the like - yes, vaccines no unless the circumstances are "special" - to mean a very agressive dog which needs special handling (catch pole, etc) in which case the owners are thrilled to have us take care of it out of their view. :O)
I personally would not return to a clinic that did such routine, minor things in the back, away from my eyes. I want to know where a vaccine was given, insure that it WAS given, etc.
As for owners handling their own dog - it is not a matter of whether or not we want them to - it is a matter of liability. I have been privvy to an owner, who insisted on handling their animal, get bit. Care to guess what the owner did to the practice? I am paid and insured to get bit by an animal, it stands to reason to let me do my job.
Besides most folks are so fawning and appeasatory to their animals, they make them worse, which in turn makes them doubly worse the next visit, which in turn makes them tremble in fear at the very thought of being in a vet clinic for the rest of their lives. Best to just calmy have a seat, let us do our job and create a confident animal not afraid of other people handling them and not needing mom to stand over them telling them "it's ok to quake in fear, good doggie!".
I think if you are feeling uncomfortable in something as routine as vaccines, you will not feel comfortable with the spay, no matter how many people you ask. The fact that you are asking - is a red flag you need to find another vet.