I'm sorry to say I don't do style and I don't teach it, and if you want to be a better skier, you will have to sacrifice style on the high altar of improved balance and mileage!
After burning up the miles you will eventually start to develop a style of your own, It will be unique and like a fingerprint. People looking up the mountain from that favourite restaurant in the sunshine will say 'Look, there's George - I can tell him a mile off! Get the waiter and order his dry martini would you Clarice'.
There are several ways to improve your balance but no short cuts to perfecting it. Balance depends on a combination of mileage, at what age you started to ski, and whether you have done any similar sports that need really good balance such as cycling or riding horses.
If you started skiing as a very young child, your balance will have come naturally, and there will be no concept of skiing being 'easy' or 'difficult'. If you started later in life, your balance will not become second nature until you have skied a very long way. You will have to rely on muscle power and fitness to hold you up and hold you steady at the start. This reliance will decline as your balance improves.
What also helps considerably with your balance is thinking about where your weight is at any given moment, and the type of snow you are skiing on.
To improve your balance initially, try keeping your skis about four inches apart, rather than together. It matters not how close the instructor has his skis. He is only trying to look stylish. It may be a little tricky keeping the skis parallel without them crossing, but they will soon grow out of this. Get a little lower down too by flexing your knees a bit more than usual and bending at the hips. Think about your weight. The default position is always over the middle of your foot.
The wider stance also gives you more latitude with your centre of weight, which can swing to a certain extent between the two skis.
Once again, concentrate on keeping your weight right in the middle of your feet unless told otherwise.
As you have probably never thought about where your weight is on your feet even off skis - after all it