It sounds like youmight be over squinting with your non dominate eye. It doesn't take much of a squht to weaken the non dominate eye and keep it from wanting to take over.
I'm left handedn and left eye dominate. Some years ago I had Tim Meigs maken me a double shelf bow. I started alternating shots, left and then right. I wore a centerback quiver, a shooting glove on each hand, arm guard on each arm.I would shoot left, step forward, drawn and shoot right hand. I had to squnt my dominate left eye "SIGHTLY" to keek if from trying to take over when shooting right hand. My goal was to become proficent enough to shoot a deer no mater which side it came in from.