I have found that many instructors when they come across an opposite eye domination problem resort to the Catholic nunnery method of teaching shooting techniques.... beat it out of them (aka I've never encountered this before so I will make them learn the way I shoot).
I remember one of my first encounters with opposite eye dominance. I was an augment instructor for SFAUC, standing out on a range in Bragg and watching this CPT shoot and as I was watching a group of about 5 I kept going back because something was off about this guy and after about 5 minutes I realized that he was shooting rifle with his left hand and pistol with his right. I talked to him about eye dominance asked him if he was comfortable shooting like that and let him get at it. He had never really shot 2 gun CQB style before and just didn't have time on the gun. His accuracy was more a function of other fundamentals like grip and trigger pull.
No use in fighting it unless you just can't get it and everyone starts nicknaming you "Escopeta Bob", "Shotgun" (This may or may not have been a similar nick given to my 1st TS), or John "couldn't-hit-the-side-of-a-barn-from-2-ft-away" Smith or something to that effect.
My Mother-in-Law is LED and Shoots Righty with the gun moved slightly left to her Dominant eye. I gave the basics, did an eye dominance test on her, gave her instruction on Safety and fundamentals and shot with her several times. She was a very accurate shot and a good student. I told her not to fight the eye dominance, and that it would just make it that much harder. For a Vacation, my In-laws went to a shooting course and the instructors tried to break her of shooting like that. She told them that her Son-in-Law was SF and he taught her to shoot like that and that she wouldn't change for them...they left her alone. She is very matriarchal
