You may be able to see what your sister should be doing differently. That doesn't mean she will see the same thing, or act on it if she does see it. I'd guess that your care of this little girl has probably been wonderful for her (even though you can't see it yet, 3 being such a challenging age, and inconsistent care-giving making it harder).
But you've reached the end of your rope. That suggests to me that your sister has taken advantage of you long enough, and that all the energy you're putting into raising her child for her is probably enabling her to slide by with minimum attention. Daycare may be some help, both to give you a break and to introduce your niece to other caregiver's styles. She's possibly on the verge of becoming social enough to play with other toddlers, but chances are good she's not quite there yet. Nevertheless, it could be worth trying.
If you are exhausted by your niece's behavior and frustrated by your sister's lack of parenting, you could back out of the arrangement and ask her to find other caregivers. This could throw her into a state of crisis that would wake her up. But I would expect not. So the question probably becomes, "Do I remain as a positive influence in my niece's life?" If you decide yes, you might do well to brush up on the newest knowledge about parenting effectively. There are some excellent books to help you:
A great starting point is The Happiest Toddler on the Block, by Dr. Harvey Karp. You can also watch a few quick videos about his approach: http://www.youtube.com/watch?v=fJ1428uYs2g&NR=1&a.... . He demonstrates exactly how he "speaks" the toddler's language so they know he's heard the need they are expressing. This calms them and makes it easier for them to cooperate.
A website that offers loads of tips and positive suggestions is www.askdrsears.com.
Good luck. I hope you move toward a future you can live with.