Handedness is in the spinal cord, not the brain. Whether to use the left hand or right hand is being decided by the fetus before the spinal cord and brain connect - according to this:
https://www.sciencedaily.com/releases/2 ... 095904.htm
I thought I once read that the brain grows from the spinal cord. This sounds as though the brain is already developing and then makes a connection to the spinal cord. Right? That is not the gist of the article. Just that the suggestion of one connecting to the other got my curiosity stirring.