I am fifteen years old, so I can totally relate. I first became an aunt at 11 years old, and thought the same things you're thinking. I know it's hard when you live very far away and can't be with them. I just recently was able to see my brother and nieces (2 and 4 years old) and we bonded greatly.
Here are my tips from being in your situation (and still currently being your situation....almost totally across the country from them):
- Call, text, and video chat as much as possible. For those in this kind of situation, technology is a beautiful thing.
- Send lots of cards and letters for holidays. Remember their birthdays and maybe send little gifts from time to time. You don't have to spend tons of money or shower them with material things, but they appreciate little books and cards they can enjoy. We always send books to the girls at holidays, like little Christmas books at Christmas and Valentine's Day books at Valentine's day, etc.
She won't resent you, I promise. I hadn't seen my four year old niece since she was six months old, and naturally she didn't remember me at all. And trust me, she was a tough nut to crack. It took a couple of days for her to realize I was a nice person and just wanted to play. I goofed around with them, played, sang, and interacted. Getting down on the floor, playing, reading books, etc. make the best visits and give them the most memories in my experience. Just watch a movie with them or send a cute book you used to love. Little things have made the most difference in my relationship with my girls.
She just won't understand who you are, so be patient. Just play with her and continue to reiterate that you're her mom's sister, and she'll eventually understand. My niece kept asking Who's Aunt Sam? every time her mom mentioned me that way, and she'd point at me and say Daddy's sister. She eventually got it and by the end we were great friends and she enjoyed my company and called me Aunt. Like I said, it just has taken time for me and technology really helps keep a relationship when you live as far away as we do.