Is it legal for owner sign up paperwork that the person they are giving the pup to cannot take it to a certain vet or the owner will take it back if t

Animal law is NOT a specialty of mine, but I believe a seller can chose who to sell to and not to sell to (based on the pet being allowed inside, etc.) and possibly subject to terms they specify in a sale contract, but (1) once they sell the pet, they cold possibly sue the buyer for NOT honoring the terms of the agreement, which licensed vet you take the pet too is most likely not going to be an inforcable issue and the seller bad mouthing a particular VET would open them up to potential issues they would NOT want to face, i.e. "Defamation Per Se".  There are Attorneys who specialize in animal law, I would suggest you google that for more focused advice, but such a specialty may carry with it a charge for a consultation and advice.