My son is an anomaly. He does most things right handed, so I bought him a Ruger 77/22 to learn with & cut the stock to fit him. Off to the range we go and...he throws the rifle up to his left shoulder. Long story short, that is what feels right & natural to him. No problem. He reaches over the gun to work the bolt & it doesn't bother him. Go figure. And since he shoots from his left side, he simply closes his right eye, even though that is his dominant eye. He shoots well, hits what he wants & it works for him.
Eye dominance is not an issue unless we make it an issue. They just have to shoulder and shoot whichever side feels correct & close the eye not being used. Seriously. That's all there is to it.
Having said that, some kids have AMBLYOPIA, which means one eye literally doesn't SEE as well as the other. This is not an eye dominance thing, per se, but for these kids you must train them to shoot from whichever side has the "good" eye. So a right handed kid who has amblyopia in the right eye is best trained to shoot from the left side. Yes, its awkward at first. It'll take some time. But it is for the best that they learn to shoot using their best seeing eye.
Hopefully this made sense. Eye dominance matters little when both eyes can see equally well because a person can shoot from whichever side feels right and natural and simply close the eye not being used. But a person with amblyopia has one "good" eye & that is the eye they should use, no matter what & that might mean shooting from the non-dominant shoulder/side of body. It just takes training & time.