I'm going to tell my 13-year-old sister that she needs to grow up
Why do you think she needs to grow up?
Her behaviour is starting to get out of hand.
Telling someone to "grow up" is very petty and disrespectful, trying to seem you're more mature or like you're above the other person. It's best to treat the other person how you would like to be treated.
My sister needs to grow up. She can't live under my roof forever.
Ease up on your sister, she is only 13 man. There is plenty of time for her to grow and mature. Let her be a kid while she is still young.