I was shocked by how bad Gusto was at the vet the first time. It wasn't a case of "I never handled my dog before"; I could clip his nails, touch him all over, manipulate him. I hadn't quite realized at the time how different Gusto In Public is from Gusto In Private. He was screaming so loudly when they tried to draw blood (thank heavens he's got stellar bite inhibition) that people out in the waiting room commented on it, and the vet finally gave up and said "We'll just do the heartworm test when he's neutered in a few weeks".
Peanut butter on a tongue depressor wound up being the answer for him. He wouldn't take cheese or anything like that, but the peanut butter, he could start on before anyone tried to touch him, and keep going as the blood was drawn. Not a peep from him, and there's never been an issue since.
My dogs do not get taken from the room for things like a blood draw. If the vet has an issue with it, I will find a new vet. Meg, who is the easiest dog on the planet at the vet, and doesn't even need to be restrained for anything, goes into a full panic if they try to take her out back. When she got out of her collar and wound up in the chair behind my back, that was the end of it. Blood draws in the room, and with Gusto I'm pretty clear that it needs to be done by the person most likely to hit the vein the first try (sometimes the vet, sometimes the tech). Meg is a little more patient and will let someone work a bit to find the vein.
I'm very grateful to the wonderful vets and techs we've had, who will take a second to feed some treats or visit before diving in. I know their schedules can get backed up, but it makes it easier so much nicer for everyone. I've only ever had one vet who was really brusque and Gusto hated him. One of the big selling points of my new vet is that Gusto was actively seeking attention from both her and the tech - huge for a dog who mostly thinks people are to be ignored.