This is a very old thread.
If you are a new rider, this is a question you need to ask your teacher. At my first riding school I was told that the horses were trained not to move forward unless you used your leg. This isnt the way I now ride but it was thought safer for beginners.
If the RI says you are doing it right, than believe her. She knows the horse.
The cutting of corners will happen if you let the horse's head turn inwards. You may be looking inwards to. Control the angle of the head with your outside rein. Dont pull on the rein as that will stop the horse.
As you ride round the corner, try po picture what the horse has to do. Its outside legs have to take bigger longer steps than the legs on the inside. It takes more energy from the horse so try to relax and breathe deeply. It will make it easier for the horse.