Geeeze some vets are just so not GSD people!
it is perfectly normal for your puppy to mouth, by nipping you and other dogs she will learn bite inhibition. Learning bit inhibition started with her litter mates when she would bite too hard and the other puppy would either tell her off or walk away leaving her on her own with no one to play with. You need to do the same and your older one will instinctively do this. This is normal learning behaviour. In order to learn this, they need to mouth!
Some Vets are not interested in assisting pups with learning or helping with aggression, so it is always a good idea to have your puppy focus on you when the vet is fiddling with her. I have always done this with a heap of treats in my pocket and commanding the 'look' and then rewarding. I have also held my GSDs head towards me. I have never ever had an issue, however it is best to be cautious.
Also, something to think about, if you are not happy with this vet then go to another one, hopefully you can find a vet experienced and comfortable with German Shepherds, because not all Vets are and finding one that is makes a huge difference.