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The proper way to shoot with a scope is to have both eyes open. It takes lots of practice to train your eyes to do what they need to do. With your dominant eye looking through the scope your 'weak" eye can see the area around the target and where the bullet is going.
Military helicopter pilots use a helmet with a different display for each eye, it is how they can fly when "blacked out". they see totally different things in each eye.
It takes quite a long time to train your eyes to see different things, but it can be done. Practice and more practice! I wish there was a magic potion that I could give you, but the only way is to keep practicing and don't give up.