Not sure this really matters, but my original post suggests my girls are 4 years apart, and they're really only 2 years, 10 months. (I don't know why I said little DD was 9--brain glitch!--she's actually 10.)
Thank you for the replies. We did have a discussion about the problem again last night and I've come to some conclusions. I'm going to try and separate the girls as much as possible, try some positive reinforcement and also some consequences. There is a dynamic at play that I believe can be reversed, but it's going to take some work on everybody's part. And believe it or not, even though it's big DD who's being the snottiest here, it's little DD who carries more influence. Little DD is a better communicator, has a stronger personality and can influence the mood in the room far quicker and far more blatantly than her older sister. Little DD also has an interest in finding a solution to the problem, whereas big DD claims not to--she just wants to focus on how much she wants little DD out of her life right now. Little DD can be very difficult to live with, but she also can be a very positive influence. Just this morning, she had big DD eating out of her hand after one very polite, respectful exchange. Little DD was purposely being friendly, in hopes of solving this problem, and big DD isn't the type to be rude in a vacuum. At least not for very long. So my strategy is to "use" little DD's interest in improving the situation to help her continue to take the high road, to try and keep the girls separate as much as possible, to crack down on abuse with severe consequences, to continue to help them find outlets for their irritation that don't involve berating or abusing each other. Like someone else said, I understand the feeling, but I will not tolerate the behavior.
I am the younger of two girls, and my sister and I have an okay relationship now, but she was pretty awful to me when we were kids. She even says today that she's surprised I'm willing to be friends with her. And I am willing to be friends, but I'm not eager to be super close. I do not feel that our parents helped us AT ALL in our relationship with each other, and it might not have made a difference even if they had. But I'd at least like to help my girls here, even if for no other reason than to get our household back on a more peaceful keel.