Scratch:
If you shoot well with a rifle using your left eye, then it would surprise me if you are cross dominant. Cross dominant is not "screwed up" and doesn't mean you have a "bad eye." Most people who are right handed are right eyed. Most people who are left handed are left eyed. But lots of folks are cross dominant. I don't know of any way to "fix" this since nothing is "broken." You just adapt.
Regarding the eye dominance test, I suggest doing it slightly differently. Hold both your hands out in front of you, with your thumbs away from your fingers in sort of an L-shape. Now overlap the fingers and thumbs of your two hands so that you make a circle between your hands (darn, the picture from the NRA books is a whole lot less confusing than my description...). Look at something across the room and put it in that circle. Now bring your hands back to your face. The circle should come back to your dominant eye. Repeat this several times.
The reason I suggest doing this test with two hands, rather than one, is that using one hand might bias you to coming back to the eye on that side of your body.
If you are shooting your pistol using an isocolese hold, then it doesn't really matter which eye is dominant. You can move your hands slightly one way or the other to line up with either eye. If you use a Chapman or Weaver hold, you might have to tilt your head to line up your right eye with the sights.
If you are shooting one handed with your left hand (and you are sure that you are right eye dominant), then you might want to tilt the top of the gun about 15 degrees to the right to line up the sights with your right eye. Note that if you just push the gun over to the right while keeping it vertical, it will break the alignment of your left wrist and make it difficult to control recoil.
Of course, if you learn point shooting, it won't matter at all ;-)
I suggest that you try to eliminate issues one at a time. First, try shooting the pistol from a bench, with the frame on a rest. Sight the gun in on the target as you normally would. Now close your left eye. Does the image change? Now try closing your right eye. Once you've determined your dominant eye, keep the other one closed and fire some shots while concentrating on your trigger control. Are the shots still going to the right?
Finally, it's also possible that the gun's sights are simply off. Do you know anyone nearby who is a good marksman who could take a few shots from your gun?
M1911