Guess I get to be the bad one and say there is no possible way on earth to stay away from the idiots!!! You have to get the horses attention on you and not the other riders. Yep it's really tough to do but there will or can always be bad situations where you have to have the horses attention on you to keep you safe. Was recently on my colt at an event and a gentleman on a huge horse was being an idiot basically running all over everyone else and I had to say something cause he ran into me a cpl times. If I'd been on my older mare I would have pulled the lariat off and start swinging about a 15' loop and if they aren't smart enough to stay away from me they'd get lassod! Not my problem if they are idiots. If it's colts I can understand control issues but not acceptable if mature horses. You have to keep you safe and that means being able to control your horse in all situations. Unfortunately that's awful tough sometimes. Should also add that this is why I like a bit of spirit in a horse. If dingy bob decides to let his horse stick his nose up my horses bum and my horse plants a well placed kick, not my problem. I don't allow my horses to do that to another horse. Again colts are a bit different at first.
I have ridden and shown both young horses and stallions, and yes, your horse has to focus on you, BUT I never had a horse run backwards and slam into my horse before, with that rider hooking my horse, hard enough, accidently, to draw blood. Any horse is going to react as if he was attacked, and nothing you can do about any prevention, in a situation like that!
I have had kids run their mares, right up under my stallion's nose, and I always had control of my stallion, even if it was another rider's fault, as that just goes with the territory if you show a stallion
Any yes, it is your problem, and you will be at fault, should someone get his horse's nose up your horse's ****, and your horse kicks and nails that person. That is the way law suits work!
At one open show, I took a three year old stallion for some show experience, and since he was going well, put him in a large open class. Some gymkana people were using that pleasure class for a warmup.
Okay, my stallion is going nicely, even with horses crowding him, passing at speed, running laps, but the cincher came when some idiot decides to pass me at speed, , passing against the rail and my horse, with barely enough room to squeeze by. He them proceeds to lope another out of control round, coming up on me again, at which time I told him, 'pass me on the rail side again, and I will kill you'!
You have to be in control of your own horse, even if someone else does something stupid
Experienced people can also accept the challenge of riding in heavy traffic, but it is not okay to subject some beginning rider to that, taking lessons, like the OP. I am surprised that her trainer did not have that arena booked for a lesson, versus giving one under those circumstances!