I am left eye dominate, shoot handguns right handed, shoulder arms from the left shoulder.
I always shot using my left eye, so I sort of cocked my wrist slightly (shooting two-handed) to compensate. I had some photos taken as I was shooting, and noticed my right forearm had rotated ninety degrees to my left and my wrist had "broken" and the gun's muzzle near vertical in recoil, and that my shooting hand had jumped clear of my left supporting hand. No big deal, the muzzle was no where close to my head.
After cataract surgery some years ago, I began using my right eye. This kept my arm, wrist, and gun in a more nearly straight line. Now, shooting in this manner, my hands stay together, and there is less "breakling" of my elbows under recoil, and the muzzle is more like forty-five degrees.
As to my shooting I noticed no difference to my accuracy, still a matter of sights and squeeze.
This was really only noticible with very heavy bullets and powder charges, especially in cartridges like the .45-70 or .454 Casull.
Bob Wright