A horse doesnt need to know how to neck rein to barrel race. But it does need to know how to break at the pole, flex laterally, collect/extend, move its front end,rear end, and ribcage independantly, and, of course, whoa.
ok I get what you mean. And no she doesnt do that. I'm also working on that with her but short of holding a pail of oats by her side she wont turn her head that sharp. She acts like it is impossible for her head to turn that sharp unless of course there is oats in the deal.
Sounds like she's reluctant to give to the bit. The easiest way, that I've learned, to establish a good lateral flextion is to start with a rope halter. (rope halter will hit pressure points on the head requiring the horse to give to the pressure)
Stand at your horse's side at about the shoulder. Ask your horse to bring it's head around by reaching with the lead up towards the wither. If your horse brings its nose around at all. Even a little bit. Release and reward.(not treats...just a pat on the neck and vocal praise)
Gradually build up the lateral flextion. You don't want to have to fight. You want as little effort as possible.
After the horse has learned how to do it in a halter, graduate to a snaffle and do the same.
Lateral flextion is very important for any dicipline. If your horse doesnt give to the bit its going to get very ugly (not to mention dangerous) in a dicipline like barrel racing.
What bit are you currently riding in? Do you have a video of just flatwork?