Just know that they aren't machines, that some are easier for some things than others, and some of the stuff we do to them is unpleasant and seems pretty unfair from their perspective. I'd correct and calm and manage but not be angry about a reluctance to get a shot. You've done medicine with toddlers, I imagine.... their ability to understand of the benefit of shots is far better than a horse.
Some vets have more patience and better horse sense than others. The one I have now can get a lot more cooperation out of a horse than some I have had, just by his calm manner. But I will sometimes cover their near eye with my hand and talk and distract for shots, it helps them not tense up before the shot, which makes it easier to stick the needle than if their muscles are all tense. With teeth, the vets themselves are usually better at managing their head and I stay out of the way. If they act up too much, like my pony, we sometimes corner her in a stall.
She wasn't bad at all except maybe for that little bit of foot stomping afterwards. I've read they do that with nervousness though. He was really fast with the shot. The jumping after done. I just rubbed her head. She didn't get a lolly pop but I had her pellets and Texas tea waiting:')