I have always been extremely right-side dominant - eye, hand, leg, etc., but used to have decent hand/eye coordination on both sides. I always shot right handed but cataract surgery left me with near vision in the right eye and outstanding distance in the left. This really messed up my coordination for a while but I had to get used to it. Unfortunately, I couldn't see the target or game with my right eye without a scope so I was considering switching sides. However, two years after surgery and my right eye is trying to take over again. If it continues to improve, I may be able to stay right handed with open sights.
My wife is right handed and left eye dominant. She shoots a pistol well but cannot handle any type of long arm. It's scary to watch her even pick up a rifle because she is so uncoordinated with it. However, she will grasp a pistol naturally and just move it over to the left side. I taught her to shoot decent groups on a standard 25 yd target in one afternoon and over the years we've lived in the country, she has killed a few varmints with a handgun on those occasions when I wasn't around to do it. I pity the fool who breaks into the house at night if I'm gone - she will shoot and ask questions later - unlike some parents, we always told our sons to make lots of noise when they came home late... :winking: