Hello,
Despite the fact that i don't have you seen skiing, and only based upon your description, i have following advise.
It is realy a matter of pressure on the sidecut of a ski. Normally at the end of your turn you could reduce the combined force of forward pressure and lateral kneeforce directed to the top of the mountainside. Not only the forces on your knees must be correct but also the position of your hips and thighs. Try to maintain them as still as possible. Do not sweep your hips thru the turn. A major frequent fault is also rotating the shoulders towards top mountainside. Via your back degree any rotation of shoulders or even at level of hips will be translated in a force modification at your knees. Any changing factor will be transmitted via your knees and boots onto the ski's.
So, i'll hope this will get you closer to non-slipping turns.