C.S.
I feel your pain! I have a 16 yr old and a 13 yr old. Oldest is very nice to everyone except me and her younger brother. She won't share much with me either, and she is mean to her brother, so I relate to your situation. Hopefully, for both our families, a lot of this will pass with time and maturity down the road.
Some of it may be more than just teenage grumpiness. You mentioned that your oldest girl has been through a lot in the last 3 years and that she has been upset about her younger sister since age 6. Maybe she needs some help that a mom can't give. Maybe a short-term with a counselor or pyschologist (without you there) could help her learn ways to cope better wtih her life and to see you as a resource, not as her enemy.
I also suggest that just the two of you to go away together for a weekend, someplace she picks, where you can just do something fun together, something you have in common. While you are there, talk with her about all the things you love about her and admire, with no conversation about what you don't like. She needs your love now, even if she is actiing very unlovable. A trip alone with you will show her she is important to you.
After that (not on the trip), I would calmly explain to her that the only way she will be allowed to go to social events, especially if you are driving her, is if she is civilized at home. Even if she is angry, she has to speak nicely to you and her younger sister. Otherwise, stay in her room until she is ready to be polite. You cannot force her to like you or your other daughter, but you can make her behave better at home. Try www.loveandlogic.com for ideas for dealing wtih this.
Both our oldest childrn need lots of love. We have to put our own hurts and disappointments aside and give them the love they need from us, even when they themselves are not being loving. At the same time, they also need us to make it clear that they cannot be allowed to be mean because that is not good for them or others. It becomes a habit that they don't know how to get out of. It can be stopped or at least minimalized if we tell them it is no longer acceptable and they cannot go anywhere without being decent at home first. Even when our oldest girls start driving, they are still minors and cannot do things without our approval. This is not being mean. Legally, these kids are still under our care and it is our jobs to raise them into functioning adults, which includes learning to be nice even when you don't want to be.
Given that your daughter has been upset about her sister (and you) since age 6, that has to be resolved. Get outside help with that, for her sake. My daughter has some issues she has to learn to deal with, too, and I will start her seeing someone this fall. In a couple of years, we won't be able to make them go to counselors, so now is the time.
I wish you and your family all the best!