Re: How to improve the left hand.
I like to use analogy a lot, but think of it this way, if you are weight lifting dumbbells, are you going to lift 25lbs with your right arm and 15lbs with your left arm standing in front of a mirror? Nope. But, I think you know this already, which is why you are asking this question.
You just have to use it more any way that you can. Not only does the arm itself need more conditioning, but so do the neurological connections in your brain, which is why you need to put "miles" on that side of the body as Bachman suggested. That'd be my take on it. I need to get in some more miles myself.
I see my light come shining