No one is saying what their videos ARE- it would help to avoid repeats!
This one is my favorite- Cupcake the Herdmaster from Blue Star Equiculture- he's a little bay mini, and this is his own movie with a very peppy cupcake soundtrack song- he's trotting in the snow at liberty- chasing a sleigh. My kids love him and he has a FB page too.
Did anyone post the one from that trick trainer girl in england with the pony who fell down while running antics around her? The pony knows some airs above ground tricks. The girl/woman is cracking up wearing wellies. She also has a drafty chestnut horse in other vids, a belgian or haflinger.
I think it's not so much a rear as proper levade-ish maneuver. And no maneuver should be out of bounds. You never know when the pony might get stuck on something and could be helped out of it by a controlled stand up. Also, yes kid would be better off to learn to remain organized when horses do something other than walk calmly in a straight line.
It was pretty clear to me that the pony was being controlled by cues from the adult off camera. The child was just sitting there, and was not teaching the horse to rear. The pony was performing a series of dressage steps culminating in that levade.
I think your observation is good, but rather than not show the video to a child, I think it would be good to discuss that portion so he knows not to teach his pony to rear.