Praise be to Allah.
We appreciate your concern about this issue, which is indicative of a high level of piety, and your keenness to raise your daughters in chastity and purity. This is an obligation that Allah has enjoined upon fathers and mothers. It is important to pay more attention to that upbringing if the Muslim is living in a land of kufr (disbelief) or he is living in a Muslim land, but his family are kuffaar (non-Muslims), because of what is involved in that of a great deal of corruption and a lack of helpers and supporters.
We invite you to think about two things:
that it is possible that your good relationship with your sister’s daughter may be a strong motive for her to become Muslim. If that happens then it will undoubtedly be good for you, for her and for your family. She may need you more at present than she did before because of her weakness and her need for someone to help her with the hardships and difficulties of life. If she sees you treating her kindly, that may have an impact on her and she may become Muslim, and be saved from an eternity in Hell.
That if you cut off ties with her and forsake her, that may be a cause of her turning to evil people and their getting close to her; her actions may become more offensive and their effects may – Allah forbid – even reach you because you are her relatives. It may be in your best interests – as a family – to prevent evil and corrupt people from attracting her to join them. Then you will have the reward of preventing those evils from becoming a part of her life and thus protecting your family from the harm that evil people may do to them.
This is what we would like to draw your attention to. But if she is of the type that will not soften or respond, and her evil outweighs her good, or there is no goodness in her, then we think that you should cut off ties with her.
And Allah knows best.