Right-handed, left-eye Dominant

[Mistman]

My third grandson is left handed, right eye dominant. He's also small for his age but very athletic. While it felt odd to him [at first] using a right hand finger on the trigger, he's done as well as the two older grandsons. With both hands on the rifle or handgun, and both eyes open, it wasn't a matter of arm strength to hold steady. He's 10 now, and likes shooting a .223 off the bench. But shooting from other positions he prefers to shoot .22lr and .22wmr as those rifles and handguns are more manageable for a kid his size.

Same here, mines 10 also and will shoot 17's and 22's all day but gets anxious and anticipates recoil/noise shooting center fire, even off a bench. I'm not pushing him, as long as he's shooting and enjoys it he'll come around to the bigger stuff when he's ready.

 

[Wombat of Doom]

My son is the same. Right Handed Left Eye Dominant. He shoots left handed and works the bolt with his right hand. His AR throws brass across his face with out hitting him though it is possible some cases could come back at him. He seems to have accepted it and is making it work. He hasn't considered retraining his eyes.
For shooting single rounds in a RH bolt gun while shooting LH, he has an advantage with the port facing him. I am jealous you can shoot with both eyes. Sometimes I have to close my left eye just so my right eye can see better

left handed ar uppers are so nice if you shoot lefty. I have several scars on my right forearm from hot brass hitting it and searing on. The stag uppers have been awesome in that regard. I can only shoot rifles lefty. The CX4 is a very cool ambidextrous platform I have to recommend to other southpaws.