This seems like an extremely rare incident. I would suspect a bad batch of vaccine, and presumably the veterinarian involved will be looking into it. Such a painful loss for you. I do hope that you find a way to heal your heart and comfort your children. The breeder must be devastated to lose three puppies in such a tragic way.
There is a take away message here. We never expect "routine" vaccinations will bring tragedy, but it does happen. Years ago I was in a Vet's waiting room, the client ahead of me had just left. She returned and asked the receptionist for paper towels, as her dog had just vomited in her car. Amazingly, the receptionist supplied the towels and did not alert the vet! I asked what the dog had had done, and the answer was vaccination. I yelled at the tech and the vet that they had a problem and they hurried out to the parking lot, returning with the dog which they took to a back room to work on. He recovered from a vaccine reaction, but it was touch and go for a few minutes. The client might have just driven away......and lost her pet. Reactions like this are not common, but they do happen and can be life threatening.
There is a reason humans are asked to wait a few minutes after receiving a flu shot at a clinic. In my experience, most veterinary offices do not request this after shots, but they should. Always keep a close eye on your animal after these "routine" office visits if any medication has been given. Any unusual behavior in the days following vaccination should also be a red flag. Auto immune reactions can take a while to show up, and can be very serious. If the dog seems to be a little "off", you need to pay attention....