For your heelside turns, you might be swinging your back foot out a little too quickly, which results in more of a plow than a carved turn. Get some speed up (nothing crazy), then slowly transfer your weight to your heels and bend your knees. Let your board "slice" through the snow and keep it on its edge, traversing rather than sliding down the hill. When I do it slowly like this, I can almost feel the board "take" me through the turn on its edge. You'll be going sideways, so eventually you'll run out of space and need to transition to toe, maybe even just stop at the end of the heelside carve and look at your track.
BTW, I'm not an instructor, just a fellow 2nd year guy who likes to get better every time I go out.