This sounds like the perfect time for you to read Kevin Lehman's "Have A New Kid By Friday". You are at the point where you need to pull the rug out from under this behavior NOW. The book is not long at all...2/3 of it is scenarios, a playbook, if you will, with great ideas for dealing with this type of behavior using "reality discipline" (aka natural consequences). In short, he would tell you it's time to whip out the "Vitamin N" - for NO - at every turn. Don't do ANYTHING for her. Don't take her anywhere or include her until she starts behaving like a respectful member of the family. Rock her world by nipping all of the entitlement right in the bud. She goes nowhere and does nothing until she can behave properly.
You don't need to be snippy or petty w/her when using "vitamin N"...you keep calm and be matter-of- fact. Say it, turn your back and walk away.
DD: Mommy, can I have / go / do...?
You: No, sweetie. <Turn and walk away>
DD: Why not?!
You: I don't like the way you screamed at me in the car. You know we don't talk to each other like that, so no, we're not going until you can talk respectfully and kindly.
DD: Ok, sorry! Can I go now?
You: I appreciate that, but no. We can try again tomorrow.
Stick to your guns and allow each day to be a new start. If she throws a tantrum, relocate her to her room and tell her she can come out when she's ready to behave like a part of the family. If she throws a tantrum in public, leave IMMEDIATELY. This is going to be a pain but she needs to get the message.
Be consistent. Be strong. It's worth it...try to imagine what the teen years will be like if she doesn't get a grip now. You can do it!
ETA: I don't mean to sound unsympathetic about the divorce or anything else that's concerning her, but the fact is, there are acceptable ways to express yourself healthfully and there are others that aren't. You can't make any positive headway with her before breaking through the behavior, so I would start there. I also agree about the food...additives, colors, etc can have a dramatic effect on some children's behavior. Also, make sure she's getting enough rest. My son is a different kid altogether when he's tired...everything is so much worse.