Kudos to you for looking for wanting to be a better shooter and for asking for advice.
I agree with what's been posted, especially by melchloboo. I'm a big believer in dry fire. You can do most of what you need to do at home without even firing the gun. It's not only productive, it's a lot cheaper than sending lead downrange.
As far as the cross dominant issue, I'm a leftie, right eye dominant and learned to shoot rightie. I also practice leftie shooting, in which case I turn my head so I can still use my right eye, though it does tend to shift the POI to the right a bit for some reason. Experiment to see what works best for you.
The only other piece of advice I have I posted on another thread:
http://www.thefiringline.com/forums/...4&postcount=33