You can only register puppies if both parents were registered. That's also the only way to prove they are purebred. If you took them in to be registered, didn't you bring the parents' papers? Poodles can be born with rear dewclaws. They can also be born with short tails. But since this litter seems exceptionally off I'd guess the parents weren't of any good quality and shouldn't have been bred. I'm thinking this breeding was quite irresponsible. You also said the female was getting older, how old is she?