As with a scope, a dot sight sight won't make any weapon more or less accurate. When using iron sights one is trying to see/focus on the front sight, rear sight and target. The dot sight eliminates the rear sight becomes a bead on a shotgun - sorta. While you can focus on the front sight with both eyes, the dot is only seen by the master eye (on a pistol). I have not used one on a rifle. My first instinct was to focus on the dot and let the target blur. After much experimentation and listening to others I now focus on the target and let the dot be blurry. Just as your eyes will find the center of the rear sight (using irons), your eye will find the dot.
Also consider the size of the dot compared to the size of a "normal" front sight. It is much smaller, therefore precise. Using dot sights take commitment.
For a change try putting painters tape over the front of the sight. This will force one to use both eyes and use the weak eye to focus on the target.
Here is an interesting article (to me anyway).
I have found that many shooters think entirely too much. This is not rocket science, because if it were, I would not be a shooter. Hence, I am not smart enough to shoot badly. When Erich Bujung was the Olympic Pistol Team coach, he always said, “No stinking thinking. The mind is a terrible thing...
www.ssusa.org