Forgive me in advance for saying something you may already know. But, on the chance you haven't considered it, let me mention how the eye is changed during cataract removal and artificial lens replacement.
The (original, biologic) lens in the eye is supported by a ring of muscles. Those muscles contract to change the shape of the biologic lens that our eyes come with. That change in shape -- a flattening of the lens -- makes its focal length change to adapt to objects at varying distances; from inches away from the face to infinity. The brain does all this contraction and shape changing automatically to bring any object, at any distance, into sharp focus. As I said, forgive me for telling you something you already know.
When the lens gets cloudy over the years, it is said to have a cataract. The lens loses its ability to contract and become opaque as the cataract 'grows'. So, the cataract is removed and replaced by an artificial lens that is fixed in focal length -- usually set up to be infinity. The brain can no longer make the shape of the lens change to work optimally at varying distances.
Pistol sights are not, of course, at infinity, or even very far away from the eye when the gun is at battery. So, the eye with a replacement lens cannot actually focus at this distance. Some form of supplemental magnification has to be used -- just like when reading.
The perception of focus is also affected by how much light is being admitted to the eye. The iris of the eye is also a ring of muscle and it changes the size of the pupil to adapt the eye to the amount of light that is transmitted. The important part of the size of the pupil, for the shooter, is that, as the pupil is made smaller by the contraction of the Iris, the DEPTH OF FIELD of the image at the back of the eye is increased. The smaller the aperture, the greater the depth of field. That means that a wider range of distances is 'In-Focus' as the aperture is made smaller. For a third time, forgive me for saying things you already know.
Finally, eye dominance is something the brain does and is independent of the visual acuity of the eyes. The brain will NOT switch to the "better" eye. Eye dominance is fixed for all intents and purposes.
The solution!!! I'm gonna guess you've been using dark glasses while shooting. I'm gonna guess that because most of the shooters I see in matches are using dark lenses. The works against good shooting, in general, and particularly makes the depth of field on the retina very shallow because the Iris is opened by reducing the amount of light coming into the eye. When the Iris gets bigger, the depth of field becomes very narrow, and, in the case of a person with a fixed lens, making only very distant objects sharp to the shooter's perception.
But, increasing the amount of light (wearing clear or lightly tinted glasses) is not sufficient to bring the pistol sights into focus for those of use who have replacement lenses. We also have to add some amount of diopter (magnification) to focus on things that are only 18" from our faces.
You would benefit greatly from a good set of specially prepared shooting glasses. Go to Walgreens and find the end cap with the reading glasses. Hold your arm out and stick your thumb up. Try on readers until you find the diopter that allows you to see all the little lines and details in your thumb nail. It will be somewhere around +2 Diopters plus or minus a quarter diopter. You won't be able to bring any objects further away than five feet into focus. But, all you care about as a shooter is the front sight. There is no other component of reality for the shooter.
Now, knowing your "correction" for a proper shooting lens, have a pair of shooting glasses made up with lightly tinted lenses with the right eye at this diopter setting and the left eye set for infinity. At a match, put your glasses on early. Your brain will quickly adjust to the strange, new world you've created.
I could have just said this: you need some proper shooting glasses with a correction for close vision for your right eye.
I would recommend DeCot HyWyd as a company with decades of experience helping people like you, and me, (aka, Shooters) with glasses that permit better sight acquisition than ever before -- even back in the day when our eyes did most of this work on their own -- or, gave the illusion of doing so.
No other, single purchase has improved my shooting as much as has getting proper shooting glasses with right eye, plus diopter correction and a light tint that allows greater light transmission.
Of course, the targets will be blurry with these glasses. That's all to the good. Remember, targets are just a seduction, taking your attention away from where it needs to be during a match -- on the front sights of your guns. So, good shooting glasses will also help you be more focused on what's really important in a gun fight -- the sight on the barrel of your gun.