I too am right handed, left eye dominant, shoot handguns right handed, long guns left handed. Most of us with this condition have found that in order to shoot with both eyes open it is the best "only" way. He is young enough to teach properly before bad habits develop.
I am the same, only I'm messed up in everything, I bowl right handed, golf right handed, throw a ball right handed, shoot a pistol right handed, write left handed, and shoot rifles and shotguns left handed. But I am in fact left eye dominate. I guess I can write with my right hand too, just isn't nearly as neat and clean as my left hand writing is. And your right RobertT, I've found that keeping both eyes open is what works best for me in trapshooting.