I would not be on either side of a deal that didn’t have the Bill of Sale and payment be directly between buyer and seller.
If the trainer wanted to buy the horse and then sell it to the parents 10 minutes later for double the money, I suppose that’s their business. But to use the parents’ money as a deposit and then resell the horse to them at an inflated price? That is sleazy. It also doesn’t quite look like the trainer was “adding any value” to the horse to justify the increase in price. All of that reeks of ripping off their own client. No one should want any part of that.