Ah that is cool! I never knew about dominant eyes. What you described is my case exactly. Different prescriptions for each lens in my glasses, and the image shifts a bit to the left or right when I change which eye is covered. I usually default to my left eye even though it is apparently the weaker one.

Fun fact. If your eyes don't work together you see like this all the time because your brain ignores one eye constantly. So you see two different images with both eyes.

Source: my own personal experience cause for some reason or another my brain never developed the ability to see with both eyes at once and reform the separate images into one. So it decided to constantly ignore one eye. It's like being blind in one eye all the time. But I can still see out of both. I can "switch" to seeing out of one eye or the other. Weird.

So I'm a chameleon?