NyaChan, I'm sorry you're upset, and I understand why you are, but I honestly don't think you need to be. No matter which of you and your sister is in the wrong - and that's assuming that either of you is, and that it's not just one of those family things that blows up because of a difference of opinion - it is not your mother's business. You are not out of order in telling her, politely, to keep out of it, which is what you did. I don't think you were out of order in telling her that you were insulted that she was taking sides without ever hearing your version, and I certainly don't think you did anything wrong in planting the idea that perhaps your sister needs to apologise to you and not you to her.
I second Marbles' suggestion if the matter is raised again: "When she's ready to apologise, I'm sure she'll call."
Important point here: if your mother's feelings are hurt it is NOT YOUR PROBLEM. Say that out loud, several times. She wasn't part of the original argument, so she doesn't get a vote about it. The only people who do are the 'combatants' - you and your sister - and you get to sort it out whatever way suits you. Your mother is entitled to her opinion, but she's not entitled to have anybody pay any attention to it.