I too, taught both of my sons to ski when they were three years old. I use that term "taught" loosely because in fact I simply controlled their environment by choosing appropriate terrain, weather, and snow conditions, warmth, etc. and allowed them to imitate me. "Watch me try this" without ANY technical jargon. We did not lean over one ski or the other, we simply pointed the wedge where we wanted to go. This of course triggered complex movements to balance and turn but did not require any conscious thought or involvement from them. I kept them on easy terrain where the learned to seek speed rather than control it. After a couple days I introduced terrain variations that induced pressure and edge angle changes.
Their progress was so natural and unabated by me. In fact I DID NOT and have not TAUGHT THEM ANYTHING! My oldest son (9) is skiing double blacks and looking for airs. The whole time I have just skied with him and introduced more difficult terrain as I felt he was able. It was his idea to ski the double black avalanche chutes though, not mine!
MY POINT IS, IF YOU JUST GET OUT OF THEIR WAY THEY WILL PICK UP SKIING QUITE NATURALLY. Most ski schools put their most inexperienced teachers with children. Why? because it really doesn't take that much to have success with kids just patience and guidance in a ripe environment.