Okay, Madeline --there are some things that should happen first.
The first thing you need to do is calm down, like BrokenWanderer and Aino both said. It is impossible to think clearly and rationally about anything if your mind is clouded by rage. And what you need, from what I can gather from your post, is rationality and clarity.
This brings me to the second thing you need to do. You need to take things from your sister's perspective. Approaching a situation from every perspective is the best way to handle things, in my opinion. People generally have a reason for something they do. Aino went into most of the possibilities here. You need to sit down and have a good talk with your sister, and get her perspective. And do not, absolutely do not lose your cool with her during this. The best way to get to her heart and discover the cause is with love. And don't lecture, that never works. Believe me, I know

I've been lectured many, many times about mistakes I've made, or things I could have done better in my life, and being lectured is the quickest way to shut me off to what's going on. Make sure it's a conversation. Oh, yes, and try not to be too harsh. I think that being firm, but loving will win the day here.
I also agree with trusting in God and Christ that they will bring this to the right outcome, and that you do need to change your attitude about this. In the long run, her decisions affect her and her only. Granted, your mom will have to pay the court costs, and seeing filthy, wrong text messages is embarrassing to the family, but your sister will be the one that loses the most in the long run. She will be the one going to a juvenile delinquent camp or whatever, she will be the one who loses credibility and friends because of her texts, she will wind up all alone if you and the rest of your family abandon her in this time. You need to be there for her, be a strong, positive role model, and show her caring, now more than ever.