Behaviour at the vet can be facilitated by the owners; for better and worse. ;)
Dogs need to know that you're confident in this situation. Be sure to remain confident and to only praise positive behaviour. Many people inadvertantly whip their dogs into a frenzy by saying in a soft, whimpering type voice: "Oh it's okay, be good, good puppy, it's okay...." while petting them.
Meanwhile the dog is scrambling on the floor, excited, and getting more stressed! Why? Because they see that their owner is uncomfortable, they're upset and whining and praising them for scrambling on the floor and getting stressed!
Do not pet or acknowledge any other behaviour than perfect, clam, collected and pleasing behaviour. When they're sitting nicely, calmly say good dog and a confident pat.
Dogs will feed off of your own energies - if you're calm, they'll remain calm too. Often a dog will be 'taken into the back' to be held by a technician at the vets. The vast majority of dogs are fine and don't require a muzzle in this situation simply because they're not being praised (unknowingly) by their owners for being upset. Away from their owners, they become calm again, remain confident and behave wonderfully (many, not all).
I'm not suggesting that this is why your dog wasn't behaving, but wanted to give you some insights that may be contributing to it. :)
As for the leaning over, I agree that strangers should not be leaning over your dog. It's a very dominant move and strangers have no place doing so.
However, if you lean over your dog, they must accept that. If you have control of your dog, they need to trust in you that YOU'RE taking control of the situation and that they don't need to worry.
As the others have mentioned, I would highly recommend going back for more obedience work and socialization. You can never have enough! :)