Okay, just had time to sit and watch your videos several times to see what is going on.
First, before getting started, to clear up a very common misconception, carving is a fairly advanced type of turn that uses only the sidecut of the board to turn and has virtually no skidding at all. It will be a while before you are actually carving a turn so don`t even worry about that right now. What you want is to get more fluid in your skidded turns and then make them more dynamic.
From a board up analysis, the first thing that is obvious is that you are primarily pivoting your board to turn it. Generally, you are traveling down the hill in a fairly straight line and pivoting the back and forth to control speed rather than riding out full completed turns.
Next, moving up your ankles, knees and hips are quite static. You have a fairly decent stance with some decent knee bend, but it really does not vary throughout your turns. In addition, you are favoring your back foot as evidenced by the fact that there is consistently a lot more knee bend in the back leg than the front. In order to pivot the board, you momentarily shift to the front foot and slide the back foot laterally to slide the tail of the board around. Moving up from there your hips and shoulders actually look pretty good and are pretty well aligned with your board. Your are not riding with a countered stance to face forward so keep this up. The only thing I would say is to straighten up a bit. You tend to ride bent at the waist a bit and this is a big part of your heelside problems. As for the arms, try to keep them a little lower down by your sides. As for the head, it is also very static. Turn your head a little more in the direction of each turn to help set up your upper body for turn initiation.
Some things for you to work on that should make some noticeable differences in board performance:
Front Foot Steering! For these skidded turns, lets use the front foot more to initiate each turn by twisting the board at the nose more. Press the toes down to pressure the toesdie edge for initiating your toeside turn and mash the heel down to pressure the heelside edge for your heelside turns.
Shifting your weight forward to make the front foot heavier is going to make a HUGE impact on the how responsive your board is. Also consider this; the heavy end of the board always goes down the hill first. Keeping the board nose heavy is going to make for much cleaner turns.
Flex and extend!. As I said, you have a pretty decent stance and it is really an ideal neutral to always return to but you need some movement throughout your turns. For right now, I want you to flex down to your lowest point as you initiate each turn than gradually rise up through the turn through completion then drop back down to make the next one. You should be rising and falling throughout every turn.
For your heelside turn, sit down more into as opposed to trying to lean back. This will give you a lot better balance and the ability to pressure the hell edge. Increasing forward lean on your highbacks can help a lot too. For the toeside turn, avoid the intuitive temptation to bend over at the waist. This does really bad things to your balance. Instead, drive your shins forward into the tongues of your boots and push your pelvis forward while slightly arching your back to stay centered over the top of your board.
Throw in a little rotary movement for your turns!. When going into your heelside turn, pull the front knee forward toward the nose of the board. This action creates a little bit of rotational movement to the foot that favors the heelside. When going toeside, roll that front knee slightly back toward the tail. In addition, pull the back knee toward the tail. These movements will add a lot of rotational force to your feet that favors the toeside.
Along with this idea of rotary movements. be sure to turn the head more, especially foe heelside. Look over that front shoulder more and it is totally okay to allow a little bit of hip and shoulder rotation to set the front shoulder over the edge you are turning to.
Turn Slower!. Right now you are very quickly pivoting the board around. Using the techniques offered above, be a little patient and allow the board to twist, then tilt onto its edge more and ride the turn through the turn more, making larger radius turns that are more completed and resembling linked C shapes.
Play around with these techniques a bit and shoot another video...