Okay. I'm the friend Neon is asking this question for. I think I should explain it a little more clearly.
Flicka rides well almost everywhere except for the indoor arena. She is fine there, will walk and trot. I've gotten her to the point where she comfortable on the ground walking through all of the corners, and to where she is comfortable walking there with me riding. When I bring her intro a trot and we are on the wall, she gets a little quick because the sand hitting the arena wall makes her a little nervous. She will go through all four corners if we are going clockwise, but when we are going counter-clockwise she shies from the far left corner. I can't "ride her through it", because she shies before she gets there when trotting. I know she is balanced enough to do it. She will turn her head and body away from the corner, and try to completely avoid it. It isn't a "spook" necessarily. She doesn't run away from it - she refuses to go into it. The few times I have gotten her through it at the trot have I praised her and ended our ride.
Someone mentioned her relaxing on the ground. I've gotten her to do that.. the licking and chewing included. She is fine at the walk UNTIL we try to trot through. She is fine with the corners in the outdoor arena.
I've been patient and worked through it with her on the ground and at a walk. I have worked on not anticipating the spook and completely relaxing. That doesn't seem to be the issue, but I have worked on that and keep it in mind while riding =)
It may help by saying that when we got her she was very nervous. She would grind her teeth, paw, kick, and bite. She is also a scaredy cat. I don't know her history at all. She is OTTB and is around eleven. She may have been a riding horse for awhile and learned to bully her rider. I do think she has issues with trust, but we are working on that =) She very rarely does any kicking, biting, or pawing anymore. Never grinds her teeth. She has improved a lot and if we could fix this I'm sure we would both be a little happier.
I don't know what else to say. Any more suggestions?
You've all given very good answers so far, so thank you =D