Advice on Move Tool Control

I’m using Sketchup 2021, but this happens in every version of SU that I’ve used. When moving something with the Move tool, I have nearly no control over the size of the movements. Sometimes, even the constrain buttons don’t work properly. See my example: I’m trying to align a sleeve on a shaft. No matter how slowly I move, how carefully I position it, I can never get it to stop flush with the surface of the shaft. It’s SO frustrating. I waste so much time trying to get things positioned just where I want them, but it almost never works out right. Can someone offer any tips on fine movement control please? Thanks.

this is because you click anywhere on the object to move, the error comes from there. Sketchup will align the point where you clicked with a surface, edge, end of the drawing where you want to end your move.
The best is to always click on 1 end and to move the drawing on the end (or edge …) of the other drawing.