I'd just like to point out that she said this was a ONE TIME THING, and that she's only TROTTING her around the pattern for fun. I don't think this horse is quite cut out for barrel racing, yes- the main reason being that, judging from ONLY that video, she looks uncomfortable. HOWEVER, all you have to judge is this one video- the people who KNOW this horse and work with her have stated that she is healthy and has a bit of a bucking habit.
If she wanted opinions (sorry I chipped in mine, lol) on whether she had a good barrel racer or not, she would have asked. She may not have been quite clear enough in the OP, but she has made herself crystal clear now- opinions are NOT wanted, she is not trying to make this horse a barrel racer, and she is not pushing this horse past its limit.
I will repeat- According to her posts, she is taking her to TROT the pattern for FUN only ONCE, so it shouldn't matter if the horse likes it or not- she is NOT doing it again.
I apologize for sounding so nasty.