Are you looking for a critique or just showing a video?
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Same question, but I guess I'll give my two cents anyway.
Coming into the arena, you are on the WRONG lead. That's not an issue for a finished horse, but for a horse who is just learning, you (as the rider) need to set them up for success and get them on that correct lead. If you need to circle him a few times before you start your run to get that correct lead, do it.
Your pocket size going into the first barrel was fine, but then you allowed him to blow the backside. If you allow him to take the end of your turn wide now at this point, you are creating huge bad habits. Perfect practice makes perfect.
You need to FINISH the turn; don't let him drift away from it.
Also, when coming into the first barrel, I do NOT see any change in your body language. You should be sitting your weight down in your seat, to ask him to rate and collect for the turn.
Also, your reins at TOO long. Look where your inside hand is when you are on the backside of the first barrel turn. It is at your KNEE. That is too long, first of all, and you are having to pull too far back, and way too far down. Shorten your reins and keep your hands up in an invisible box near your saddle horn.
Same thing on your body language when you get to the second barrel. YOu are leaning forward the whole time, and literally caught your horse off-guard because he had no idea he was supposed to turn. I don't blame him, because your body language told him to keep going forward (learning forward, no weight in the outside stirrup, etc), rather than turn the barrel.
Again, wide backside turn second barrel. Do NOT let him do this at this phase in the game, or you will constantly be fighting this bad habit the rest of his career. Bad habits are easy to create, but hard to get rid of.
At home, you need to circle each barrel 2 times (minimum) or more until he's is completely focused on the barrel you are turning, and not thinking about the next one until you are actually on your way there.
I won't say anything about the 3rd barrel, because it's the same repeat of the first two.
He does seem to be listening to you more at this show, than your last one, but you as the rider need to start helping him out. Use the correct body language to prepare him for the turn. Send him to the barrels on the correct lead. And do NOT let him drift out on the backside of a turn.