Sounds similar to my old barrel mare...towards the end I had to force her into the arena and when she finally got in she would run great...or not one time she grabbed the bit and ran straight down the wall taking out the timer
so they had to stop the timed events and go to roping while they tried to fix it.... I stopped racing her after that and she still had problems going into the arena. She didnt have problems with crowds or loud speakers or anything because she was also my show mare so she was used to it but I couldnt get her to relax in the arena so what I did was brought her stable mate in with her and ponied her while riding her buddy. Once I saw her relax doing that I rode her bareback around, and eventually got my barrel saddle on her and rode her around...it took alot of slow collected movement, flexing exercises and random patterns but eventually she started to look at the arena as just another place to work...she still doesnt like seeing a barrel pattern set up though
Some horses just really don't like doing barrels and even when theyre good at it theyll refuse. My mare was like that and I've retrained a few that were like that.
On another note, we have a gelding that is terrified if people are in the grandstands above his head or if he hears a loud speaker. What we did to fix that was got those fog horn things and bummed the use of the loudspeakers at the fairgrounds and I rode him in the arena while my friends and my parents made a bunch of noise in the stands, and ran back and forth and stuff...eventually he ignored the noise and they were able to get right up in his face and shake cans and clap and whatnot....took awhile though.