If you move too slowly from A to B, the measured distance between them will change due to absolute error up to 10m or more. The time the measurements are taken is very relevant.
No, it isn't.
What you have is a relative error in the position of A, and a relative error in the position of B. Your (unrealistic) expectation is that if you move fast enough, the relative errors will cancel out. They do not. Ever. Under any circumstances.