Is there a dominant gene for right-handedness?
There is a lot of information at OMIM  - too much to summarize here - regarding the genetics of handedness and links to which hemisphere of the brain dominates (in an individual), to schizophrenia (slight association with non-right-handedness), and to hair whorl patterns on the scalp. References are provided at the above link. Basically, hand skill appears to be a complex multifactorial phenotype with a heterogeneous background.