Saying no can be hard, but it does have to be said from time to time with all children, even those who are adults. Saying no now is necessary. You are doing the right thing. I really beleive your son is only asking because he is frightened regarding "his" dogs fate and feels guilty that he "abandoned" him to your care. He did the right thing for her before when he sent her to you. Unfortunately, emotions are talking now and not logic. I believe once a diagnosis is made, he will truly reconsider his thoughts on taking the dog back. Should he still seem to feel the need to have her once she has seen the vet, perhaps you could suggest that he consider adopting a dog that needs a home, who has been proven to be good with toddlers or adopting a pup? Just a thought.
IMO, you are doing the right thing.