The pictures were taken after I’d been driving with him in the cart for about 15 minutes. We mostly walked (trotted for a few steps for the picture) on the way from the stableyard to the path where we were actually working on driving. He didn’t really try to work with me during those 5 minutes or so, until he put the camera away. Then, he corrected my hands being so far apart. I hadn’t been doing that while he was in the cart - once I had more space available I kind of sprawled out.
I’m not sure if it’s just the angle, or if I opened the rein in that turn - I don’t remember for sure, but he certainly didn’t want me to do so. I was trying to keep the outside rein, make sure I didn’t pull the pony around with the inside rein, look where I was going, etc. He also corrected the height of my hands (they were sagging a little toward my lap), and my hands were cocked a little oddly (not quite puppy paws, but too much of an angle). He also had me bring my knees and feet together, and told me not to lean/hunch forward. “Leaning forward doesn’t urge the horse on when you’re in a cart. It just introduces tension to your neck and shoulders, which makes your connection less elastic.”
I haven’t had a chance to get the reining machine back out of the storage unit yet - I plan to on Sunday, since I’ll be out of town tonight and tomorrow.
He said that the breastcollar needs to be below the point where the neck goes into the chest, because otherwise it will interfere with the pony’s breathing, especially when he is in draft. It needs to be above the point of the chest, because otherwise it lessens the pony’s power for pulling, and can interfere with his movement. In the pictures, it does look too high - at the time, it didn’t seem to be. He’s the one who harnessed the pony, I just held him while he explained the process.
He asked me if I knew how to half-halt, and had me explain what I do when I give one (engage my core muscles, possibly squeeze my shoulder blades together if I need to give a stronger one, and give a slight squeeze with the outside rein with an immediate release forward, but not throwing the rein away (usually - sometimes a teacher has had me half-halt on the inside). He asked if I’d ever rode a horse down a hill who was a bit on the forehand, and got a bit rushy, and asked me to explain how I asked the horse to slow down and balance, and said that it was the same idea when driving.
He didn’t really discuss body position as it relates to weight, just that in going around a turn (especially a sharp one at speed) that the driver (and navigator, if applicable) want to shift their weight to the inside so that the cart doesn’t overturn. He said he would go into more detail later, but wanted to mention that much.
I’m definitely not claiming to be a good driver this quickly - he just felt I was doing very well for my first time! He said that most of his new students wind up weaving back and forth a bit drunkenly, or don’t have good control of the whip, or try to leave the reins slack and neck rein (even after he reminds them that they need contact). So, he wouldn’t dream of allowing them to drive solo. He felt I had good enough control of the pony, and that the pony was very level-headed and well-trained, so he could teach me more effectively when he could see me from a couple of feet away instead of right next to me. He said that in a marathon cart, when he is navigating, he can see everything the student is doing, but I’m not ready for that yet. 
I’m curious if you have any pictures of your students from their first lesson with you (with you in the cart, of course) so I can get a better understanding of what you feel I should be doing at this stage. Of course, I’m no where near as good as anyone who has been driving for months or years!
If you feel he is unsafe or incompetent, then I’ll definitely reconsider doing lessons, but he’s the only driving trainer I’m aware of locally who has access to horses (most work only with people who own). I’m fine with just sticking to riding/vaulting for longer, but I really enjoyed the driving lesson, and was looking forward to learning more.
I think I’m using a little too much inside rein here, but after a few times through, it got significantly better. We also worked on some circles, and “gates” made of two barrels or two ground poles. 