Personally I would not let my vet give 3 lots of jabs. They take a lot out of a dog's immune system, especially a young puppy's.
Tohme's suggestion is a good one - ask your breeder for details of their vets, call their vets up, and explain the situation. Ask if they can give you the 2nd vaccine. You can either take it to your vet and ask him/her to inject it, or you could take your pup to your breeder's vet for the 2nd jab too.
There are several reasons why your vet is saying this: It could be because your breeder's vet and your vet use different manufacturers of vaccine. Although the different manufacturers' vaccines do work together, they have not been tested and definitively proven to do so, so in order to cover his back your vet may be insisting that the jabs are begun again from the beginning.
Have a look on the records which your breeder should have given you, from their vet - it should say what the make of vaccine was, that was used. What vaccine does your vet use? Phone up and ask. If it's a different type, that's probably why. You need to obtain a 2nd vaccine which is the same make as what your breeder's vet used.
I doubt very much that your breeder's vet would have given the vaccination at 6 wks to the whole litter, if that was too young. I've heard of pups being given first jabs at 6 wks before, so it must be in the guidelines for whatever make of vaccine your breeder's vet used. Perhaps your vet's vaccine has different guidelines - that doesn't make the first vet wrong.
When you have found out what make of vaccine your breeder's vet used, and your vet uses, you can look them up here: http://www.noahcompendium.co.uk/Compendium/Overview/
That will tell you details like at what minimum age they should be for the first jab, when the 2nd jab should be given etc, for each manufacturer.