Hand preference has nothing to do with the hemispheres of the brain. Hand preference can be observed in foetuses during the first trimester of pregnancy, meaning the preference is expressed by the spinal cord before the brain motor cortex is connected to the brain. It appears that hand preference is determined by asymmetrical gene activity in the spinal cord.

You could Google the article titled Right -handed or left-handed: Why? Published in Science Daily's Research News for more information.