With the jump up thing, just rush him backwards quickly till he falls over backwards. He'll be quite surprised at that, and will be reluctant to repeat it too many times.
I understand about not wanting to send him away. The whole point is for you to learn to teach him.
If he's really unruly now, to where you'd be overwhelmed in a class, have the private lady come out and work a few sessions first, then do the class when he's ready to have those added distractions.
Sounds like you'd think the classes were fun together time, and that's good. They are fun if you look at it that way, and if the instructor is any good :~D
You will find in talking to the instructors that some are geared toward training family pets, and some are geared toward training people who want to compete in obedience shows... really, for now, you want the first. The second will be worried about a lot of stuff that doesn't matter to you, like if he sits straight and correct, when you just want him to sit and stay put :~D