Hi Mikey--welcome to EpicSki, and to the world of today's great new equipment! (I must warn you, though, that your chosen screen name may cause you some slight problems with a few of the Bears who have a notorious "Mikey" in their past. What do you think Wigs, Todd, Ott? It CAN'T be!)
Anyway, to your question--it is a very good one, and a very common problem. You've gotten some great advice above. I'll just add a couple things to consider. First, you must be clear that "angulation" is not a substitute for "rotation." Rotation, which refers to twisting the skis into a skid using the upper body, was indeed a common, much-practiced method for initiating a turn not too many years ago. It is still an effective way to get the skis skidding. There are several alternatives to "rotation" that can accomplish the same thing, but "angulation" is not among them.
"Angulation" refers to movements of the feet, knees, hips, and spine that control edge angle, and has always been important in skiing.
The only reason you would "rotate" in the past was to get the skis skidding. That is still the case! The difference is that it is easier than it used to be to get the skis turning without twisting them into a skid. But chances are pretty good that you, or something deep inside you, still associate that skidding sensation and sound with "turning." Make the movements of a perfect modern carved turn, and that "little voice" will think something is missing--so you will resort to the movements you are used to to bring back that old familiar sensation.
I don't know, of course, if this is your problem. But believe me, it is far more common than many people realize. Carved turns feel very different than intentionally skidded turns. And they accomplish very different things. Most importantly, carved-type turns are OFFENSIVE--they allow you to control your line, to go where you want to go. Skidded-type turns, which you are presumably used to, are DEFENSIVE--they act as brakes, controlling speed directly, but like a car skidding off the road, they entail some sacrifice of line/directional control.
So it may well not be the MOVEMENTS of carved-type turns that you are struggling with. It may be the outcomes of those movements. You will have change your definition of "control" somewhat, allowing yourself to glide faster while taking comfort in the increased control of your line. And you will have to USE that new-found directional control to make sure you ski a line that eliminates the NEED for speed control! Carved turns do not control speed well by themselves, so you must ski a slower line than you did in the past if you want to ski the same speed (slower line = more complete turns, perhaps even finishing uphill). If you start a new turn needing or intending to REDUCE your speed, you are highly likely to twist your skis into a braking skid, whether you want to or not!
Perhaps above all, these things explain why others have recommended that you practice "carving" movements on very flat terrain at first. The best place to practice them is on a trail you might normally straight run, a trail where you have no need for speed control. When you move on to more challenging terrain, make sure you complete your turns FAR more than most people do--start the next turn only when you feel like your speed is TOO SLOW--not too fast or "fast enough." When you point those carving, gliding skis downhill, they will gain speed (obviously), so make sure you expect, accept, and WANT that!
Have fun, and keep us posted! We'll forgive the past transgressions of your fellow "Mikey"....