Why does my mom do this! 10 points!?

I have started to feel my mom plays sides. I'm 16, and my sister is 10. Whenever I'm around my mom she is nice to me, but then whenever my little sister is around she jokes meanly about me. I think she does it unintentionally. So anyways today she told my sister how she is acting like me when she wouldn't let my little brother play with a tea set. The way she said it made me sound like the worst person alive! It was such an insult! This is not the first time she has said this, and she will try to tell me she didn't mean it like that, but she does! She makes me feel like such a terrible person! Trust me I give my little sister stuff all the time, I am a kind person, even though she constantly will steal ALL my stuff!!! But my mom makes her resent me. My mom must think I'm a loser and she can say anything like that. Do you think my mom plays both sides? Do you think I need to get a backbone? And how?