C.,
I have first hand experience with this--from the child's perspective, being raised by my aunt and uncle since I was nearly 4. Everyone else has good ideas in that you need to remember you are dealing with a child, not your sister, so I won't belabor that point.
But you must know, as the adult, YOU have to snap out of it! You're in a hard position. I get it. She's a teenager with anxiety and hormones. I get it. But YOU are the adult. YOU cannot take her outbursts personally, just like you don't with your son. I DO understand that it's different with your own child, but C., you took her on and you are in the role as her parent. DO NOT TREAT HER AS YOUR NIECE!!! A niece is someone who comes to visit then returns home to her parents. YOU are in the role of her parent now and that comes with hard days and great days. She WILL appreciate you later in life, I know, but there is a big difference between intellectual appreciate and heart-felt appreciation. I appreciate the sacrifices my aunt/uncle made for me and my sister but from day one, they treated their kids differently.
When you're a kid and things don't "work out" with your own parents (my mom died and my father let my aunt/uncle raise us), you internalize it and are certain YOU are the reason. Add to that the differences you see with your new siblings and how they're treated, especially by someone who CHOSE to help you? I wonder if you're making your niece feel burdened by the fact that you're "helping" her.
I know I'm being hard on you but I hope you understand why. This is not about you anymore. This is about the fragile heart of a young girl who's having a rough time. PLEASE sit down with her and talk with her. Maybe she doesn't like that some things you do remind her of her mom, who she might be irritated with for getting her in this situation. Whatever you do, BE THE ADULT. React to her as if her future depends on your reaction, because I swear to you, it does. Just as much as your reactions to your son are that important in developing his mind, your niece is vulnerable and still developing, too. Be mindful of that.
When my aunt, whom I also called Mom, was having difficulties dealing with me as a pre-teen and a teen, she asked our pastor for advice. He told her if she didn't give me the love I needed, I would find it where I could when I got older. I had no knowledge of this but oh my gosh, was he right. Except it wasn't love I was finding. It was comfort, which never lasted long.
A mother figure is so important to a young girl. KNOW you are shaping her, too, and you've got to be the mom you are proud of, not one who is seeking permission to slack off because this is hard more often than not. Alone time with your niece on a regular basis will help you two work this out but it's up to you to ensure that happens, not her.
I wish you so much love, C., and so much patience. I know you want to do the right thing, which is why you took her in. God will give you the strength. He's also giving you the knowledge (like when she's hurt and you think you should do more than you are) but you're choosing convenience over mothering. Be strong enough to choose more wisely.
D.