I'm thinking that perhaps, there's more to the story... They adopted out a Pregnant, unspayed dog? If they're that picky about spaying and neutering, why didn't they spay the dog themselves...?
It sounds to me, like they make a lot of money out of adopting out puppies, and they want rights to those puppies. That's what alot of rescues do-- vaccinations are very cheap, they're too young to spay, and they adopt them out for a big price-- so they make a good profit.
I suppose that it could also be that they're concerned about the puppies, that maybe they're going to give the puppies away to not-so-great-homes or something. I would be worried about that, too.
I don't see one good reason that they would take Hailey back. That's ridiculous. It was their fault for not making sure the contracts were signed. I think that the settlement they proposed today should be able to settle everything.