@M6chan , I am wondering about your claim of right side dominance. Is a strength concern, a balance concern (maybe a little of both) or maybe something else? One legged drills are clearly balance enhancing but as far as strength building, that could take a long time as some indicated above.
But, could mechanics also be a factor? Could it be that you are more comfortable initiating a left turn because the mechanics of your right foot and leg are better than the left?
If one thing is for certain from the input of others above, skiing today is no longer a sport where two skis act as one which is a very important point to understand!
The functional design of modern skis and the different forces they generate require an independent approach. In some ways, it's like how we pedal a bike. One leg lengthens while the other shortens. But unlike pedaling a bike, skiing also requires rotary mechanics of the foot and leg.
In the JF Beaulieu video below, watch from 3:00 to 4:55.
These are drills that will allow you to develop you rotary, pressure and edging skills as well as separation. It is incredible how many intermediate (and some "advanced") skiers cannot do these maneuvers when asked. I hardly see anyone practicing this yet it is very effective and a great warm up drill. And because it involves both legs you can feel the difference between what you right might be doing vs the left.
I encourage you to watch the whole video as well. Lot's of good stuff!