I have always given my own shots to all my pups as well as my adults except rabies. If I were you I would refuse giving all those extra shots!
The key would be making sure the first shot was given 3 weeks after the pups were weaned as the shot is uneffective if the pup is still protected by the mothers antibodies from her milk, which lasts another 2-3 weeks after weaned. Most EB breeders wean at around 4 weeks.
Your vets advice about the bland diet is good