Why do you want to teach direct rein (of opposition)? (which is use one backward and let the other loose)? Certainly NOT like riding a bike. What she is doing is a combination of leading and bearing. Which then can be divided into the effects. And opening/leading rein from the elbow can be shown, and a neck rein (counter bending) can be shown. Each have a place.
Don't know her age but this is a good place to start:Glenshee Equestrian Centre: The Five Rein Aids: Introduction