Human handedness results from the interplay of genetic and cultural influences. A gene-culture co-evolutionary model for handedness was introduced by Laland et al. (1995), and the present study generalizes that model and the related analysis. We address ambiguities in the original methodology, particularly regarding maximum-likelihood estimation, and incorporate sex differences in cultural transmission. By fitting this extended framework to existing familial and twin datasets, we demonstrate that accounting for criterion shifts significantly improves model fit and parameter estimation accuracy. We find stronger maternal than paternal effects on handedness, with daughters exhibiting greater sensitivity to these effects than sons. We provide an open-source Python implementation of the model, which is a robust platform for comparing gene-culture models and applying them to diverse datasets.