Is it permissible to prevent a sister from visiting her father due to the stepmother's lack of piety and her negative influence on the sister, in addition to burdening her with difficult tasks? And is this considered a severance of kinship ties? If so, what is the solution?

We advise you to supplicate for your father, asking Allah for his repentance and guidance, and to seek the help of righteous people to advise him. It is obligatory to honor and be dutiful to one's father and to treat him kindly, no matter how badly he behaves, by maintaining ties with him as much as possible. It is not permissible to prevent your sister from visiting your father. Rather, you should raise and guide her well so that you can be secure from him corrupting her.