I am so sorry about this bad situation. I tend to agree with other posters who are shaking their heads at the trainer’s behavior.
But: I think there is a good lesson in this for everyone, which is that you should always ask about the financial details of an arrangement before agreeing. It’s often awkward to ask for estimates and splits ahead of time, but I always do it precisely because I don’t want there to be a surprise or misunderstanding on the back end.
If OP wants to give the trainer another chance, then I think that should be the substance of the conversation: Not a nickel-and-dime accounting of this incident, but instead a more generous acknowledgement that this didn’t go down the way she expected and she wants to make sure that there are no more such surprises in the future. That’s a great segue to the other rider showing the horse at an upcoming show. I think it’s fine to simply say no. I think it would also be acceptable to say that, yes, that’s ok, if the rider pays everything including a pro-rated portion of the lease.
If you want to leave the barn, then, fine, go to war over the prize money. But if you want to stay, then I’d focus more on setting clear expectations for the future.