Measuring point to point distances with accelerometer

The most important part of my project is that the moving point B will be an Arduino in a box and will be handheld

I would like to have a precision of about + or - 10 cm for my project.

This just does not seem likely to be achievable. Is it the location of the handheld device that you are trying to determine? Relative to what? For what purpose?

The more details you can provide, the more likely it is that someone will have a suggestion for you.