The key is to understand why you get double vision and how it works. The fact that you get double vision is actually a good thing here. It proves that your brain is giving you access to the full image from your non-dominant eye.
When you focus on the front sight of a pistol or rifle, you get two images of the target. When you focus on the target you get two images of the pistol or rifle.
With iron sights we focus on the front sight and aim at the image of the target that is on the same side as the eye we use to aim with. For people who don't get double vision, they don't have to know which target to aim at because they are only getting information from their dominant eye anyway so they don't see two targets. The double vision is the overlap of the two images you get from either eye. If you aim at the wrong image of the target then you miss, which can be dangerous.
With red dots, you can stay target focused. You don't see two targets because you are focusing on the target. Instead, you see two copies of your gun. The gun you are using to aim with is the one that has the dot in it, but it doesn't actually matter which one you use, if you see the dot in the window then you can aim with that, either side, doesn't matter.
This is the exercise I use to train, I do it completely dry with an unloaded gun to isolate just the vision system:
Set up two targets side-by-side where the bullseyes are 1yd apart from each other.
Stand 10yds in front of the targets preferably centered between them, but as long as you can see both targets you can still do the exercise if the lanes at the range force you to stand in front of one of the targets. Use the modern isosceles stance to prevent favoring one eye or the other by position. Feet shoulder width apart. Feet, knees, hips, shoulders all squared to the target.
Aim at one of the targets using a pistol with a red dot. Open both eyes without moving and confirm that you are still seeing the red dot and it's still aimed at the target.
With both eyes open, yaw the pistol to the other target very slowly without moving your body at all. The only motion should be in your wrist. If you feel like you went past the target you probably introduced some roll or pitch as you yawed, just yaw back to the original target, find your dot and try again. By yaw I mean just turn the pistol in place, it shouldn't move side to side and it shouldn't tilt up or down or cant either way, just turn the pistol from one target to the other.
Once you can yaw the pistol back and forth and find the dot on both targets without moving anything except your wrist try closing one eye when you see the dot in either image of the gun. When you see the dot on the right image of the gun you are seeing the dot with your left eye, when you see it in the left image of the gun you are seeing the dot with your right eye.
Do this until you can reliably reproduce it using the pistol a few times, then try mounting the rifle with the red dot again. It might take a bit of practice, but your brain will eventually take the image with the dot by default because you've trained it to understand that's the important information.
