I'd be flattered they chose pictures of my horses, but I agree it sounds like they are being a bit misleading.
I had a rescue horse once upon a time and posted before and after shots on an online forum. Imagine my surprise when a friend called me a few months later asking why my horse was pictured in a magazine article about a rescue organization. Same pictures I posted, and horse had absolutely no association at any time with the rescue organization When asked, the rescue said they used the pictures just as an example of an amazing before and after. Like you, I felt it was misleading as people made the logical step to believing the rescue had rehabbed the horse in the photos.
I agree that it is somewhat unethical for the trainer to be featuring those pictures on her website...photos of horses she never worked with and, more importantly, a rider who was not riding with her at the time the pictures were taken.
When I'm looking at barn websites, I certainly realize that any horses pictured may have never been at that barn, especially if they are pictures of the trainer riding. I do, however, reasonably assume that they reflect the trainer's work somehow...either the trainer riding or pictures of the trainer's students riding while training with that trainer.
That said, I'm not sure what you can do about it. Maybe post pictures on your website of the horses, anyone researching barns in the area may see the same horses on both web sites and it would at least make them wonder.
While I understand your concern, that people don't give credit to your horses in the pictures, you should be totally flattered that your horses are obviously great and are on the website. You could probably get them to take the pictures down if it bothers you.
For years after I bought one of my horses, his importer used his picture on his business website. I was flattered, as the seller imported a lot of horses back then. And at our 2nd barn, the BO's husband used a video, without my permission, of the same horse showing off in his paddock. The website was for Porsches. Lots of horsepower there. I didn't like that, as the BO's husband wasn't a nice person, although he did restore Porsches well. But I did not request that he take the video down. I am however, still ticked off that Emory Univ. School of Law used a picture of me, along with my boyfriend (who did go there) on the front of their recruiting pamphlet for a year or two.
I cannot speak for the OP, but in my own experience, I was flattered by the importer keeping a photo pf my horse on his website when he was importing many more horses before and after he imported my boy and sold him to me. OTOH, I was upset that a man who abused his wife daily and did that in public at parties had a video of my horse as an advertisement for his business on his website.
I can imagine that someone in the horse business would not want pix of her horses advertising another barn or horse business. I don't think OP is unreasonable to not like it. But I don't think there's much she can do about it other than ask that the pictures be removed.