I don't know about teaching lead changes on your own...of course, that could just be the "worrier" in me. There is a right way and a wrong way for horses to change...but if you never need them in a show, then maybe it wouldn't matter. My gelding (I do dressage) has auto-changes from his hunter days, but I won't let him use them as he changes from front to back (instead of back to front). When we get more established in our lessons and the counter canter, we will address that.

I do lots of work on the counter canter - and that doesn't mean you have to go out and canter a whole circle on the "wrong" lead. I start out going down the rail - I leg yield him out to X and then back to the rail again, you can make your "loop" shallower if she has trouble keeping the canter on the way back to the rail. Once they are good at that you can start working on figure 8's.

Also, for lead changes, I think they are easier to teach once you have good walk-canter and canter-walk transitions. You would ride one circle of your 8, take a step of walk in the middle and pick up your other canter lead for the rest of your figure 8. Takes a lot of collection and getting them to sit back and use their butt

Play around - do you have caveletti or ground poles you could work on going over? I used riding bareback a lot to improve my sitting trot. Do you have any friends to ride with and play games? We play follow-the-leader (of course, I often ride w/ a 10yo girl) so I make little "challenges" in our games to help improve on her riding as well. Probably not as entertaining if you are both more adult

Transitions. Transitions. Transitions. That's what I work on - and responsiveness. When I put my leg on, I expect a reaction - now. Then we go out and road ride when we can for a breather/change of pace Lots of medium canter work too - bc Oliver has a sticky "go" button...

There has got to be a book out there on things to do on horse back...