I'm cross eye dominant. I shoot right handed but I'm left eye dominant. I have trained myslef to focus with my right eye when shooting both eyes open. If I am shooting a purely marksmanship course, I'll close my left eye.
When I started shoot scoped bolt guns for SWAT - I used a patch over my left eye and I trained my right eye to take over, then shot both eyes open using my rifle scope after that. My left eye would take in everything close in while my right would focus on the cross hairs and the distance through the scope.
I got some eye excercises from my eye dr. and that helped a lot.