I would never sign a contract that says the previous owner can take the horse away if they feel it is not being taken care of. That is crazy, since their idea might border on unrealistic. I would also worry that they have done this before, maybe "sold" another horse and taken it back to sell again.
The part about them having to be notified about winnings is not even close to being normal. Once an animal is sold, the original owners have no reason to know what the horse earns, unless they feel intitled to some of the earnings.
If your trainer is saying this is a good contract, what is in it for her/him? Is she/he getting a percentage of the sale? I just think that is a bit strange.
If sellers think they are entitled to being told how much the horse earns and can take it away for their idea of bad care, then they want to be involved too much in the horse after it is sold.
You get a bill of sale saying the horse is yours, the papers if there are any, plus you will know the horse is sound because you have a vet check done before paying for it.
The sellers should have no other say or demands, written or not.