Between the two threads I am astonished. You traded horses without seeing them and without a PPE, and now you want your horse back, going so far as to illegally try to get the papers back. You're upset about it and are willing to put the poor horse to sleep because of YOUR mistake. That's awful, and I don't have any sympathy for you. If you're so upset about the horse, instead of killing it off why don't you give him away or try to sell him? You aren't going to get your horse back, it's a done trade without contract.
I'm sorry to be so blunt, but you sound irresponsible and guilty about trading away your horse. It's your responsibility to go see the horse beforehand, ride it, get a PPE and draw up a contract. Otherwise, things like this happen. Please don't make the horse pay for your mistakes. His sarcoids are NOT contagious, despite what you seem to think, and they don't sound like they are serious enough to affect his health. A horse is an animal, not something to throw away if you decide you don't like it.
EDIT: mls, yes, she can't enter into a binding contract, but her parents can. They seemed willing to help out. Any contract is better than no contract at all.