Thanks for your response!

I agree and understand that stress is a huge driver of outbursts. When the initial outburst happens, I ask clarifying questions, validate how it must be hard what she's going through, about how she's feeling and if there is anything I/we need to do that would make her feel better or if she just needs to vent. I must be doing it wrong because it makes her angry when I ask questions to understand. She'll refer to people and situations that I don't know so, I'll ask who is that and where/when did that happen? That can make it worse. It's hit/miss. And then she'll rage for around 1/2 hour (Her record is a little over 4 hours). Then, later in the day (this weekend, it was 20 minutes later), she's giggling and will want to show me a Youtuber she likes as if the prior screaming/hatred never happened. It's maddening.
We are currently working with a counselor and have done parent DBT training. I have read Walking on Eggshells/companion Family Guide plus BPD in Adolescents. Our child has also completed DBT training (she said it was worthless-we thought it was awesome!) and we have all been to individual & family psychologists and a psychiatrist for the past 8+ years.
Calling a time out and walking away angers her so much. Our prior psych had us doing that. Our daughter says that when we do that, we are proving that we don't care. She says that if we really cared, we would stay and 'take it'. She screams how much she hates us and what bad parents we are. I don't think I can emotionally/physically do it anymore. It's just asking too much. I stand there, tell myself I am strong and take it while breathing and thinking to myself that this won't go on forever.
She has a 14 yo sister who hides in her room during the whole thing. She's very withdrawn. We get her out to a safe place ASAP but sometimes it's hard because of the randomness of the explosions so, she does get exposed to it.
It's just hard and it's been a particularly bad week. Thanks for reading this.