In the OP's situation I'd ask the trainer nicely why she thinks you're not going to win and what can you do to change that. Or why she's not finding a horse for you. If the answer doesn't satisfy you, get another trainer.
I agree with kayhmk.
Go to your instructor and tell her, "Hey, I noticed that you seem to like -so & so's - riding. How can I improve upon my riding skills?"
Maybe this person has a "natural talent" that the trainer is excited about, and wants to work with (which sounds bogus, but whatever). If she/he says something along those lines, then ask, "Okay, how can I improve upon my riding abilities to get myself to that level?"
You'll have to be firm about wanting to better yourself. If you want this instructor to take you seriously, and to pay attention to you, you have to be interested in your own improvement. Be sure not to start talking about this other girl- focus the conversation on yourself. Don't ask, "Why is she getting all of the attention?" That will make you sound shallow, and jealous. That's the last thing you want to be.
One time I had a lesson with my boyfriend, and the trainer gave him more attention than myself. I found out later that this was because I was doing everything correctly, and he wasn't. I didn't need the encouragement (though it certainly would have put me at ease! I thought she was ignoring me!), but my boyfriend did.
Sometimes you have to view an instructor-student relationship as purely professional. You are the consumer, and you're demanding access to a product. Your instructor should help you achieve your goals, but you have to supply the energy, and perseverance to do so.
And if this trainer doesn't give you a good answer when you ask "How can I improve?", leave. If her answer is discouraging, such as, "Well, you'll never get to that level/etc." then leave. Such a statement means that she has blinders on, and will not see your full potential, no matter what you do.
Of course, everything you do will always depend upon your work ethic. Work hard, and it'll pay off.