So interesting about the ballet styles. I had no idea!
As for the reining, I think what you're describing is the standard German-American way. The only different dressage reining I can think of is the French-Racinet style, which seems to want to avoid rein pressure altogether. I'm probably wrong on this, but that's the way it's sounded to me.
As for actually riding
the rein aides correctly, just stay close to your instructor! My experience is, I find myself doing things backward, in attempts to make it right. For example, I believe the horse
is really the one who should be taking
the outside rein, stretching into it. When all goes well, you can feel his energy swell and you can feel it coming through the rein, like asking you
how much to collect--you have his energy in your hands. But if the energy isn't coming, and/or you're trying to figure out what's the best rein length, perhaps they're too long, the tendency is to want to take up
the contact; i.e., just pull back.
There is also a difference in teaching the horse, and riding a schooled horse! All I can advise you is, keep riding and trying, and your horse, who knows what to do, will tell you when you're right.