God, OP, you are a really nasty person. she's 12 for gods sake. when you're 12 and being bullied then you do stupid things, stop being so melodramatic. yes, she needs to be punished. but you treating her like the scum of the earth isn't really going to help matters.
she's still a child, its not like she's some 18year old. i cannot believe you would call your 12 year old sister a 'lying, shoplifting, selfish theif'. yes, stealing is bad, but it could be a lot worse, and if you push her away by acting like a **** it probably will be.
at the end of the day, some people are alot more impressionable to what people think of them, and when you're in year 7??...and you can't make friends then you'll behave selfishly.
you're being just as selfish as her in the way you're acting, all you're thinking about is yourself. how YOU would never behave like this, how YOU have to put up with so much worse when it comes to bullying, how YOU feel disgusted.
she'll think back on this when she's 16 and regret it, but you'll regret it even more if when she's 16 you've pushed her away so much that she won't talk to you about anything.