My best guess is that a lot of what she is doing is age and hormone-related. Being the oldest is tough and in my own family the oldest is quite a bossy sort. She has a lot of siblings to deal with and they all look to her for guidance (yup) and probably bother her a great deal for attention, especially when you are busy with one of the others.
I constantly say to my children, "Choose kindness. It's a choice and takes as much effort to pick as meanness does." It doesn't always work (kids are kids afterall), but at least they will remember my mantra. Sometimes I get a response, even, like "I'm trying Mom," followed by a "but...." That opens communication for me to discuss alternative actions that could have been taken in the situation that were more kind.
I urge you to also provide your daughter with some "alone" time. A safe place she can be to gather her thoughts and take her own time out from her siblings. It's hard to do in a large family, but everyone deserves a haven for their "quiet time" as we refer to it in our house. So see if you can't have a "cooling down" room or solitary area of the house where (especially a teenager) a child can go to get away from his/her siblings for a while. It can be overwhelming for everyone in the family sometimes.
Just be prepared! Our oldest is twenty-eight and she is still the "boss" of the kids, which sometimes drives me batty, especially when she "parents" the younger ones in my presence as if I'm not even in the room! Keep giving gentle, but firm reminders that you're the parent and you've got it under control, even if she does not approve of your method of parenting, ultimately it's your domain and not hers. A firm "Excuse me, I'm the parent here and I'm quite capable of handling this situation without assistance or background comments," usually does the trick.
Good luck to you. You must be exhausted!