I do believe the pony's back is sore. I suggest getting him a massage of a few and some good stretching exercises. This will help him in his cart work too.
As for the kid.... He's a tough one. I did note his proper personal protective equipment.... but keep in mind safety is a first and try and avoid taking unnecessary risks. Hate to see a good rider gone to waste! Although I had a feisty pony when i was that size that you couldn't keep me off of....
Please do see to the pony's well being. He looks like a good one other then that.
Also, the saddle is forward, onto his withers. it should be behind his shoulder so his shoulder can move.
After watching closer and assessing his movement, there is most DEFINITELY back pain. I would closely inspect saddle fit, make sure the saddle is NEVER sliding forward (although I see it far too often these days).
I hope The pony is feeling better soon.
I'm not sure if i feel more sympathy for the child or the pony. Is the pony even trained for riding? And how long does this go on before one of them gets hurt, well ponys mouth probably already is, But will the pony ever trust people again? Talk about reinforcing bad behavior.