Everyone has a "sweet leg", which is the leg that they prefer to be in front when coasting along without pedalling. I think it is easier to turn corners in the direction of that sweet leg.

I personally like to ride with my left leg forward (which is my non-preferred side) and I find turning left hand corners so much easier than turning right.

Anyway, from your description of your cornering it sounds as though you are making a few technical errors which is not helping you turn well. When the corners are not tight you can simply maneuvre your body to turn the corners, however, when the corners are sharp (like a hairpin turn) both momentum and bike steering play an important role. When I first started riding I always got told to turn sharp corners as if I was driving a bus, in other words, you need to steer out nice and wide with that front wheel. Turning the wheel out wide allows you to keep the momentum going and allows you to accelerate once you have turned.

Hope all that makes sense.