First, a caveat: I'm not an instructor, just a fellow skier who has struggled with similar issues, but I do have some specific, practical suggestions I have used.
What causes one turn to be better than the other could be a wide variety of things, but (1) IMHO, strength imbalance issues should be addressed in dryland activities that are similar to skiing, in that they require a balance component--psychologically, there may be an issue about trusting the outside leg on the weak turn; (2) having a better turn is a teaching/learning opportunity; and (3) because of human nature, if you don't make a conscious effort to the contrary, dominant-leg, better turns tend to get reinforced while free skiing: If you're at the top of the steeps (or, making a sudden turn or, heck, a garden variety hockey stop) you find you always use that dominant turn. By not trusting your weaker turn, you're using it less in challenging situations, and not practicing it.
1. In the gym, do an exercise that combines strength and balance, one leg at a time. Walking alternating lunges with dumbells fits the bill there, as long as, when you step forward out of the lunge, you balance on one leg at the resting position (standing tall) before lunging forward. If that's too much of a balance challenge, there's a minor cheat that helps: You can press the front instep of the lifted leg against the calf/back of the ankle of the leg you're standing on, for a little extra help in balancing.
2. Do one-footed balance exercises, working up to balancing the same amount on each side. Just standing on a crumpled towel (uneven surface) is good. If that gets too easy, close your eyes, which makes it much harder. I have a foam roller I stand on (because it's good for fore-and-aft balance at the same time) and alternate, standing on one leg for a certain count then both legs, then the other leg. (You can get foam rollers at Jump USA,http://www.jumpusa.com/foam_rollers.html
) Or you can just practice (subtly) standing on one leg at a time, while you're waiting in line. (Lots of information about balance excercises is available on-line, in ski magazines, outdoor fitness magazines, or physical therapy sites since proprioception training is quite the modern training emphasis, and balance training is something that stroke victims, etc. often need to do as part of rehab.)
3. Observe, and learn from your dominant turn: Are you doing something differently and better on the good side? Last year, just before a league slalom race, I figured out in free skiing that the reason my turns to one side were much, much better than the other side was that I was getting lower. I applied that to both sides and jumped a whole skill class as a result.
4. In difficult situations, and at other opportunities, practice your weaker turn: At the top of the bowl, having to nail that first turn? Use the weak one. (Gulp.) Coming to a stop to wait for your ski partner? Always use the weak turn/hockey stop. First turn--always the weak turn.
Anyway, my 2 cents, worth what you paid for.
(Sitting at the computer instead of flying to race camp at Mt. Hood, because inclement weather cancelled the clinic. Let's try this all together: Think snow, not freezing rain....)