If you are shooting with open eyes, it's normal that you can't see both sights and target in focus.
I'm shooting with both eyes open, focused on the front sight. I watch it moving as I shoot and try to keep it on target and align it with the target all the time.
Now I did some experiment to actually find what I'm doing exactly.
The first funny fact is, that I seem to focus differently when using a gun and for example a raised finger. Looks like if you are looking
along something, the eyes focus differently.
With a pistol I can see the target slightly blurred but not doubled.
But even if I see the target doubled, as if trying to aim at it with a raised finger, I always instinctively know which one is the right one. Seems to me that the brain always knows wih eye is dominant.
Concerning self defence, I have read somewhere that people mostly tend to shoot without aiming when confronted at close distance which seems to be a very typical scenario. So it makes sense to practice to "stick" your pistol barrel "into" the target, so the weapon is properly aligned even before you actually look at the sights. For example in Israeli shooting system they do practice this a lot. You just look at the target, raise the weapon as if you wanted to stab or punch the target with the end of the barrel and the pistol should already point at it when it's on your eyes level.
But as a general rule it's best to do exactly what makes you hit the target. You just hear people saying what they do and experiment with it, and find what's good for you and what is not. It's the hole in the alpha zone what counts. The form is secondary, unlike the easter martial arts.
And I'm happy for that.