Your horse isn't running the barrels correctly because you have not trained him to run them. You horse has no bend, he doesn't understand what is being asked of him, he is confused, and what do you do? You JERK on his mouth, and you KICK him in the sides. I don't blame him for running off with you and not stopping, one bit. You are ruining
I'm sorry to be so harsh and so mean. You look young and you sound young and I want my point to come across good and strong. You need help with this horse. You are in way over your head, and it's only going to get worse if you try to do it yourself. You're dangerously close to having a nutty, out-of-control, crazy horse simply because you are frustrating the heck out of him and he doesn't know how else to respond.
And if any of these so-called "trainers" haven't pointed that out to you, then they aren't really trainers. Find a reputable trainer; one who has actually trained successful horses and isn't just a backyard whatever trainer. Yes, we can explain things over the internet. Yes, you can watch videos and read books. But would you want an airline pilot to fly a plane you are on, when they learned it all via the internet and videos? Absolutely not! You'd want them to have hands-on training. So why should training a horse to barrel race be any different? Hands-on training cannot be replaced.
Don't even think about barrels right now for the rest of the year. I am 100% serious when I say this. You need to learn how to use your BODY to cue your horse, and your horse needs to be trained to listen to body aids. He needs to be soft in the mouth (and you need to learn to have soft hands, and not jerk him around) and give willingly to pressure. You need to get your horse BROKE. He's not broke if you can't stop him...... and he's not broke if you cannot control his body.
Read this thread from start to finish and back again. Barrel Racing Exercises and Drills.
Your horse is not ready to barrel race. You've skipped a lot of steps in training him (not just for barrels; but regular riding) and the holes are showing through. Learn how to properly ride him first the rest of this year, get some help from a trainer, and then start teaching him the barrels again in the spring at a WALK and a TROT.
I doubt this is what you want to hear. If I were you, I wouldn't want to hear it either. But you've got some serious issues with this horse that are only going to get worse if you don't heed our advice and take the time to actually train him.