Did he come off the 1st barrel super wide, every single time? If so, the rider was just not able to pilot and get him OVER far enough to set him up for the 2nd barrel turn. Plus, you've been habitually turning him too soon, and its hard to tell in the video, but it almost looks like your body language cued him to turn before the barrel.
Note for next time, I wouldn't "punish" him by running him 5 more times
that day with other people. Rather, that should have been something for you to work on and fix/figure out at home.
Because ... it is also possible that something was hurting him. Usually when a horse all of a sudden refuses to do something, they are hurting somewhere. Has he done it since?
When were his teeth done last?
Last chiro visit?
Also, in general, in that video you are lacking body control with him. He's just kinda happening to make 3 turns. Turning when he wants to, and not in very good form. You've got to get more precise about where YOU place his body and what you ask him to do and when.
First barrel: You ran him straight at the pocket. He needs to have bend in his body to properly make the turn. Here's his body coming into the turn. Too straight:
Instead, tip his nose to the inside, and use your inside leg to push his ribcage out, and use your outside leg to push his hip inward. You want to create bend from his nose to his tail, like this:
And as you already know, ask him to turn one stride later (you turned too soon).
Also, where are you looking when you make a barrel turn? On the first barrel in that video, it looks like you are looking directly at the barrel. That's a no-no. Your horse goes where your body looks. Do you want him to run on top of the barrel? Nope! So do not look at the barrel. Pick "axis points" on the ground around the barrel where you want him to travel. And then get his feet there.
Set up some cones at home to help you with this. Measure 3 feet from the barrel all the way around and draw a line on the ground there. Place cones on the line to make it more visible. Then try to keep him perfectly equal in the turn all the way around. This will place his body approximately 4 feet from the barrel, all the way around for the turn. Yes, every horse will have his own turning style. But the 4-feet-method will give you a starting point to work from. Some horses do better with this perfect circle all the way around. Some do better with an off-set circle. Some do better with an oval shape. Some do better with a rollback style. Time will tell on their particular style.
So on your third barrel. You aimed too wide for your pocket. And then you turned too soon. Both of these things cause him to come out wide. And you are learning inward. Do not lean!
So this is my rough drawing in paint. (Trying to portray a perfect pattern.) You can allow yourself a little bit of arch on your approach to the first barrel. The arrow I drew is what you should be looking at when you head for your first barrel. That is your first axis point. Then stay a perfect 4 feet from it all the way around. FINISH the turn completely before heading on a perfectly straight line to your 2nd barrel, and finish the turn completely before even looking to your next barrel.
Same thing at the 2nd barrel. Look for your first axis point and head straight for it. Stay a perfect 4 feet from the barrel all the way around. FINISH the turn, and head straight for your next axis point on the 3rd barrel.
So work AWAY from the barrel pattern on getting total body control on him. Getting good bend and being able to tweak his body position at a moment's notice. You want 100% control so that if you accidentally turn him too soon (riders make errors ... we're not perfect) you can use your inside leg to push him away from the barrel in the middle of the turn, so that you can fix your turn while you are doing it.