Throughout the history of golf, there has been debate going back and forth about which side is dominant in the golf swing. There's the right side argument, in that this side leads into the swing and keeps the left side from taking over. The left side argument is that you do everything else with your dominant hand, so you should hit the ball with your left hand, too.
Let us never forget that golf is a two-sided game. One of the famous quotes from Ben Hogan's Five Lessons is that "as far as applying power goes, I wish I had three right hands!" (Three left hands for you. Adapted directions follow.) This isn't an entirely accurate statement of what he did at impact and is thus misinterpreted. What he meant was that at impact he is pouring it on with the entire left side. He is definitely not telling you to bang the ball with your left hand or swing with your left side only.
What Hogan wants us to remember is to get into position to hit with the left side by leading down with the right side. The swing starts down with the right side and puts the left side into a position where, at about the point where the hands are level with the hips, the left side can hit as hard as you want. Actually, Hogan says that both sides should hit hard.
Kathy Whitworth made a similar point in her book, Golf for Women. What she says, incidentally, applies to men just as well. She is very clear that the right side dominates the swing. That is not to say that the left side does nothing, but that it cannot take the lead role in the backswing and that it follows through the ball on the downswing.
Annika Sorenstam has mentioned that to start the downswing, you should have the feeling that the right side is moving into the ball and the left side is staying where it is -- that the left and right side are separating. Again, the right side is in control.
Go to the range and think, "lead back and through with the right, hit with the left." That might make things much simpler and give you some powerful hits.