Is the stepmother entitled to refuse the sister's relationship with her biological, atheist mother, and what should the sister do to please them both?

The stepmother deserves honor, respect, and dutifulness. Part of her excellent upbringing is to raise the girl according to Islamic morals, such as tolerance and maintaining kinship ties. The stepmother has no right to prevent the girl from connecting with and being dutiful to her mother, even if she is a polytheist. Allah Almighty has enjoined kindness to parents and to accompany them with goodness, and commanded connecting with the mother even if she is a polytheist. The girl should be gentle with her stepmother and explain to her that connecting with her mother is a religious obligation, and that her obedience is obligatory unless she commands disobedience.