Hi Maiasmum and welcome to the forum
Your half-sister's story is a sad one. Unfortunately it doesn't sound as if she is likely to break off contact with her stepfather or change her habits in the near future, so I hope you're successful in your application. Although you say the mum is cooperative with SS and drug workers, etc, SS must have a file for your niece as she was in care, so hopefully they will see that she's inconsistent and this is likely to keep repeating itself. If you aren't already keeping your own records, you should start now, as documentation can be crucial especially if the application will be contested.
Wishing you the very best of luck - you'll find everyone here very welcoming and supportive, as well as being a mine of helpful information [:)]