Kp and Dakotasin pretty much have said it all. You can try, but it is difficult to change a lifetime of habits.
I taugh NRA hunter safety classes for years. Every six months I'd get a 12-14 year old cross linked. I always taught the kids how to check this, you could see dads standing in the back of the class doing the same exercise. This problem is serious, because it effects things other than shooting (yes, there are other things in life). The kids I found had problem in gym classes, becasue they couldn't hit a baseball and had hand-eye coordination problems.
There are some very good eye doctors today that can give kids eye strengthening exercises. my dausghter was equal-eyed-dominant, she would use her right eye to look to the right and her left eye to look to the left. Actually she never used both, and they were working quite independent of each other. It drove her crazy in the class room, but we found the problem in 4 th grade and she is now right handed right eyed. she had 4 years on varsity tennis, undefeated in singles, but a lot of hours were spent in eye exercises.
Shotgun is especially difficult to shoot non-dominate eyed, you have to be a cyclops and keep your dominate eye closed. But it is often done by hunters. at trap contests you see a lot of guys with patches that keep the patch down when shooting to avoid the stress of holding their dominate eye closed when shooting.
When my vision loss started, my body shifted from right eye dominate to left eye dominate in about 2 weeks early in my progressive vision decline. I was amazed at how fast that happened without any effeort from me. Post laser surgery with some reduced vision in my right eye, the left eye has remained dominate. So I am right handed left eyed dominate. i use to be a pretty good wing shot, and would limit out on doves every year. Two years ago i miseed 20 straight, till I realized I was shooting right handed left eyed. For shotgunning I put a piece of masking tape over the left eye of my shooting glasses. Shotgunning is a fast sport and you don't have the time to disipline your eyes, you just react.
BEAR