Yes, your daughter is running your household. When you gave the privileges back, was it because she changed her behavior or because she kept at you to give them back?
Have you tried Love & Logic? This system is over 35 years old & it works. I first learned about it because DS' teachers in grade school used it, so I did a class with the parenting version. There are many books & videos available on the LoveAndLogic.com website.
In a nutshell, L&L allows parents to allow the child to choose from options you pre-approve & utilizes natural consequences for bad behavior. You cannot reason with an angry child; the child earns the right to speak with you only in calm & kind tones. For example, instead of cancelling your son's birthday dinner, you have a baby sitter on standby so your daughter loses the party instead of your son, & she gets charged for the sitter. No friend. No social events until the room gets cleaned according to your list or directions. In some cases, a child who slammed their bedroom door repeatedly came home to find the door removed. You don't have to come up with a consequence on the spot -- in fact it's often more effective to say you'll deal with it later while expecting her to go to her room while you get your positive energy back.
Love & Logic saved my sanity & helped me be a loving, guiding, & patient parent. DS got to the point where all I had to ask was whether he wanted to choose a consequence if he continued what he was doing, & I only said it once -- he knew I'd always follow through. (We had absolutely no problems in his teen years & he's an amazing person at 23 today.)
L&L does advise that if you are still having anger & defiant issues after 3 months of following its program, then professional counseling for the entire family should be considered.
Love and Logic works well, but only if it's followed through with, as with any other behavior management tool.
I use pieces of Love and Logic in my classroom, but the behavior management tool I really like is from a behavior management program called Capturing Kids Hearts. It's called a.social contact. Every one in the household would sit down and agree on words that describe how they want to be treated, how the adult s want to be treated, how kids and adults should treat each other, and how to solve conflict. Write he words down that everyone agrees with, and make sure to talk about what each word means (for example, what Respec t looks like). Once a contract is agreed upon, everyone signs it, and agrees to the consequences of not following it. In my classroom, one redirect is a warning, a second redirect is loss of a hall pass, third is a lunch detention. They know it's a warning because I have the warning phrases posted (what are you doing? What are you supposed to be doing? Are you doing it? What are you going to do about it? ) There's a different set of questions for disrespectful treatment (who are you talking to? How do you talk to me/adult? Are you talking to me respectfully? What are you going to do?) Make sure everyone agrees to the contract and signs it knowing g there will be consequences for repeated breaches.
For major breaches of contract, I will then turn to Love and Logic. Make sure it's a logical consequence for the crime that won't hurt anyone elses day (especially yours!) For example, I never assign kids to work during lunch for not doing their homework because then I'd miss lunch! I stead they get 75% the next day or 90% if it has a parent signature.
Most importantly, follow through! If the kids see that they can get away with things and can treat each other or you disrespectfully without being called out, then it was pointless to do in the first place.
Also, do please call the counselor. Lots of kids and adults see them these days, and there's not nearly as much stigma as there used to be. She does need some strategies to help her cope and direct her anger.