So I'm guessing you have tried the trick of pointing at something across the room with both eyes open then close one eye at a time and whichever eye has your finger on target is your dominant eye....right?
I have a dominant eye for sure but I get the same double sight or double target thing you do. It’s just how our eyes work.
My understanding about both eyes open shooting is that it’s meant for point shooting where sights aren't really used. I just focus on the target and bring the gun up into my field of vision in front of the target and fire. This is combat shooting so you aren't going to make neat little groups, it’s meant to be a quick way to hit COM -ish. (OK some mutants CAN make neat little groups like this but it’s rare.)
Point shooting is meant to use your natural pointing ability, keeping both eyes open just helps you see the situation you're in better.