I know it's hard. But, try to be her friend. When she speaks negatively about something, continue on in a positive manner. Speak positively, think positively, act positively. Walk away if she berates you. Let her know that you care. But, you can't be with her or enjoy her company if she treats you and your family poorly.
Meditation could help in keeping you calm and will give you new reserves of energy when dealing with her. Remember to breathe!
Once things are getting a little easier for you to deal with, maybe spend some time with her just hanging out and doing something you both enjoy. It's hard for someone to complain if they are having fun! Of course, you will have to build on this slowly since she is extremely negative.
You say you don't want to move out of your parents home because of her and I agree you should not do that. Even if you totally avoid her, the lesson will reappear later in time with her or someone else.
It sounds like she is being a typical spoiled teenager. In time, she should outgrow this with love and support from her family.
Good luck!
