Right hand dominant, left eye dominant is a tough combination at first. Ask me how I know.

I'll bite - how do you know?!? LOL!
When I first certified at our local range, I was *by far* the worst shot of the group. As in, for a given challenge, everyone else could have gone out for a leisurely meal, returned, and I'd still be plugging away.
Our first challenge to be licenced with pistols involved hitting 10 out of 10 22mm shots on a 6 inch target from 25 meters. The challenge took experienced shooters anywhere from 1 minute up to about 20 minutes.
It took me more than two hours to do it, the first hour in which I may have hit the target a cumulative handful of times. (Hooray persistence!) Granted, I'd never shot before, but it was still pretty terrible. Around 1 hour and 45 minutes into shooting, one of the instructors suggested a modified hold when he realized I was left eye dominant and right handed.
The running joke with the guys until I improved was that I was more accurate throwing the gun (an untested theory) than shooting. Ouch!