Work him at the pace he's going until he's ready to walk show him walking is the reward after hard work

For the safety of my family, I sadly have to get rid of my horse because he needs a more advanced rider/owner. I love him so much and would never give him up if I didn't have another option. If you are interested in giving him another chance, his is for sale at 1700. He a 15 hand spotted saddle horse and loves kids and the water. If you want to know what he looks like, he is the paint horse in my pictures.

Have someone hand walk him while your on and every time he tries to trot stop him and make him stand until he relaxs and repeat until he walks quietly and then over time have the person move farther and stop holding him as he gets better

Hi! My mare Jewels and I run barrels and I know what you mean. He probraly wants to run and run since he used to to barrel races. Maybe try a bit with more leverage or walk him in small circles, then slowly make the circle bigger and bigger every day. My mare will always slow down in small circles.

Walk him in lots of small circles so he has to slow down

Hello Isabel,
I recommend you to work on the notion of comfort with your horse, to let him know that walking is more comfortable for you but also for him.
You can begin to free walk on loose rein and when he begins to trot you can ask him some exercises, halt, shoulder in, counter shoulder in, reinback when your horse calms down, reward him directly. Repeat the exercise as many time it is necesary. The goal is for him to understand that when he is calm he won't be distubed and that he will have to work if he doesn't want to stay calm.
The answer is mainly in the idea of rewarding him as soon as he calm down :)

Unfortunately he probably got sour doing barrels so you will have to make riding fun for him again. Either have someone try to hand walk him when you are on him or take a crop and do a good tap. If he tries to rear like you mentioned and old school trick is take an egg and when he pops up hit the egg on the top of his head. Once you get him to relax and walk a bit try giving a treat with you still in saddle. Lots of praise and scratches. Just for a good while keep just happy relaxed saunter about the arena or barn area till you are satisfied and he starts walking properly again.

Maybe having someone pony the horse by leadrope while you're riding? Sorry that's all I have

He just wants to run, and when we try to halt him, and actually get him to stop moving he always tries to rear.

Does he want to run or will he not move faster than a halt? I would work with a trainer if you are having problems. Also lunge work might help!