I agree with Gwenhwyfair...take this piece of garbage to court....the AKC probably means little to her.
Hitting these creeps in the pocketbook is one of the only ways which might get their attention but most likely they will continue their dishonest practices. I would also investigate the potential for exposing them to criminal practices and fraud charges involving their "business"....this might slow them down more than a monetary loss. Your actions just might prevent something similar happening to the next individual who chooses to buy a dog from her.
Yes, maybe the AKC might direct you in some fashion as I am certain this ploy regarding "full AKC registration" is a scam they are quite familiar with....
Sorry to hear the pup's health is compromised but I have this belief that dogs show up on our "doorsteps" for all the right reasons...no matter the hardship which comes with the dog....