How to modify DNA evolution model to fit actual data?
Mutation is not a random process because there are many mutational biases, e.g. the transition vs. transversion ratio. Ideally use a proper evolutionary model. Maybe try a tool that incorporates substitution and indel models. I'm not up-to-date on the best packages, but e.g.

INDELible http://abacus.gene.ucl.ac.uk/software/indelible/
Evolver https://www.drive5.com/evolver/ (not to be confused with the PAML package of the same name)