"All crossed up." Yep, that about describes me, too. Only more so.
My eye dominance changes from one day to the next. I've done all the "figure out your eye dominance" tests, and the answers keep changing. I'm not surprised, really.
As a child, when I went to kick a ball, I never knew whether I would use my left or right foot. Nor whether I would use my left or right hand to roll dice, dial a phone, open a door, use scissors, or any of the other myriad tasks that everyone does a million times a day and that normal people don't have to think about.
Generally speaking, I am left handed at tasks done while sitting down, right handed at tasks I do standing up. But that's a very general guideline, and if a task is new to me it usually takes me awhile to decide which hand I will use to do the job. Generally I'm pretty darn clumsy, but I figure I've got good reason to be.
I usually shoot right handed and use my right eye to align my sights. But, when shooting from behind left-hand cover, I use my left hand and my left eye.
When shooting one handed, I use my left eye for my right hand, and my right eye for my left hand. (Yeah, I know ...)
I have absolutely no recommendations how to cope with mixed dominance, except to note that you'll have to make a decision and practice doing it the same way, every time.
You can use your weaker eye if you prefer, but you'll have to practice a lot more than someone using their stronger eye.
You can use your weaker hand if you prefer, but you'll have to practice a lot more than someone using their stronger hand.
Think of it as an excuse to go to the range more often and to burn more ammo downrange than other people!
pax