It sounds like you have a great start! I pretty much do everything you are saying, but I drag a tire with a whippletree so they get used to pulling the weight and having the whippletree hitting their backlegs (which could happen). Once the driving bridle is on, I long line them touching them everywhere with the whip (not hitting, just touching), especially behind the hind legs as they are walking and trotting. They should be comfortable with this as something could break or touch them that they cannot see. You dont want them trying to turn around to see what it is. I also get them to drag a container of rocks (you could tie this to a tire or pole that they are dragging.) They should get used to rattley noises...I also put a trace on the inside of a leg and get them to drag a tire (or pole, but make sure the traces are attached to the whippletree with binder twine so it can break if they panic). One of the most common driving incidents is when a horse either jumps a little or kicks over a trace and it gets caught between the hind legs. You want to make sure that this does not panic them. Once this is mastered I add a pole to either side of the tugs so they gets used to "shafts" beside them. They should be able to walk without moving away from the poles. Once you feel safe with everything I would put the carriage into the shafts but do not do up the traces. Have someone help you and lead the pony and you can line drive him beside the carriage. If the pony panics the carriage can simply fall out of the tugs and its not attached. Once there are no problems, do up the traces and have someone lead the pony until its comfortable...
I teach all voice commands such as whoa (most important!), walk on, 2 clucks to trot and a kiss to canter. I back all of our ponies to ride first, then I drive them. This way they already have the steering down pat. I can also ride all of my ponies by using my voice. I dont even need to use leg (to get them going, but I use it later on in training for bending etc.) or the reins to slow down or stop them (also used once they are a little older and ready for contact). Voice commands are very, very important since its about 90% rein contact when driving and you are allowed to talk to a driving animal in all classes.

Diamond Jubilee... do you teach driving?

My 15-year-old daughter rides, but desperately wants to learn to drive. There are some names of folks who do lessons on another thread, but they are an hour+ from Newmarket and I would love to find someone closer to us.

We're in the Newmarket/Aurora area... (sorry, out of town for a bit so didn't answer earlier!)