First off, a good resource is:
http://www.hope4aparent.com
This website is run by a colleague of mine, (I am a therapist, but don't specialize in kids)She is excellent, and maybe able to give you some words of advice.
As far as your niece, I would talk to her and reassure that you are invested in her, and will not give up on her. A regular 13 yr old has insecurities, but given your situation, your niece will likely be very insecure as her mother's death, her father's inability to step up, and your other sister's inability to handle her. While they are all understandable situations to us as adults, a child sees it as "I am bad kid, they don't want me, everybody leaves or gives up" (While I am overgeneralizing, this is a likely possibility). I would also check into grief counseling or places in your area that have resources for children that lost their parents. I am from the Pgh, Pa area and I know we have somewhere called The Caring Place, that deals with just that. When kids are in situations like this they often lash out a little as they are afraid to get close, so it may be a little bumpy at first. Hang in there and good luck, you are doing a good thing.