that is hard packed granular where I am from, not ice.
you need to use the entire surface area of your board. That means pressuring the tip and tail using the outsides of your feet and your knees. (press outwards)
also, you need to steer through your turns. Your timing is off. You are rotating fast and washing out the majority of your turn. There needs to be a happy medium between the rotation and the wash so that you are actually changing direction while rotating.
maybe think about yourself going down the hill and not just being on the hill. for example, my turn is a hook in front of me, i see exactly where i want to go the entire time. This is different from simply performing the motions that keep you on top of the board. Put more pressure on your leading leg, as a teacher i would not even care if you were doing it way wrong so long as you got used to steering with your front hip.
practice riding around with your lead leg bent and your back leg more or less straight, that should line you up with the slope of the hill and give you some shape to your turns
--not to mention a work out.