Jax was likely really surprised and confused by the odd "lesson" and happy to have things back to normal.
It sounds like you have a smart horse, which is good, but they will test their rider occasionally!
I hope this new instructor works better. Is she/he at least a USDF silver with students that have at least successfully shown thru 2nd or 3rd level? I would not bother with anyone with less qualifications.
Reading your rant reminded me of the first "Dressage" instructor I had. She was so horrible
and I was not experienced enough to know she didn't know what she was talking about!
But I did know that she didn't seem to do much except name-drop and say insane things like "There! That was a good step. I don't know what you did, but she is going better now" what???
Then I saw her at a show, a simple schooling show, and she only w/t the gelding and he was hollow enough to hold soup on his back! I never had her back to my farm for another lesson. She was worse than useless.
I changed to a USDF Gold metalist, whose students were scoring high in Region 3, and soon I was placing at every recognized show. Against much fancier horses too