Wow.
Is this behavior of your sister's fairly new...or is this more or less, how she's always been? How old is your niece? Is the father in the picture? I know that these are a lot of dumb questions, but they're relevent ones. Your sister sounds as though she's overwhelmed with stress, and is lashing out. Probably not the brightest thing was getting a dog to add to the strife. I gotta tell ya, I'm more worried about your niece (as I suspect are your parents), than I am you. You're a big girl and not to diminish you, or your feelings, but you can get in her face. I suspect that your niece....cannot. Talk to your parents. I know that money is tight for you, but offer to take them to dinner. Don't alienate them because your sister is being a 5 star bitch.