If my daughter called my DH a prick I'd have chased her upstairs myself and dragged her down myself to apologise, but I would have intervened here well before that stage.
I think you're doing what you're accusing others of, not seeing things at all from the DH perspective, you're projecting your own experiences onto a situation that is not the same at all, it's understandable, and everyone does it to a certain extent, but it's quite obvious you are doing that because you are rewriting the OP to fit in with your narrative, your minimising one set of behaviour and exaggerating the other.
DD comes downstairs to talk to her mother - nothing wrong there
"DD is 'frustrated and emotional' Came downstairs to ask me for advice."
Father constantly interrupts with unwanted and unasked for opinions and advise completely minimising DD Distress.
"he tells her she should just leave it. That she’s escalating things and should drop it (not terrible advice tbf)"
DD gets upset - doesn't seem unreasonable under the circumstances
"She gets upset saying ‘I’m not asking you , you don’t know what’s going on’"
*This is where it starts to escalate IMO, that was rude, she shouldn't be telling her father off for trying to help, and OP shouldn't be openly condoning that, OP could have stepped in here to calm down daughter, explain her dad is only trying to help and take the drama elsewhere.. inexplicably she chose not to do any of those things and let it continue.
Father continues to be a prick.
He tells her to leave it, and that there's no need to get upset
DD calls father a prick - probably not the best but again he was being one.
Completely inexcusable and past the point of no return.. nothing to do with ADHD as many people on this thread have already said, she was angry, upset and frustrated about the situation with her friend and someone basically telling her to 'calm down' and she wanted to lash out in that moment and hurt him.
With regards to the dads reaction, I'm not surprised at it, there seems to be an awful lot of pandering going on, and undermining, neither of them were having their finest hour, but I can't blame someone for losing their shit when they are so blatently disrespected by their teenager with (seemingly) their mum's blessing.
She should have apologised after the chat with her mum, he should have apologised to her then and sorted it out that night instead of letting it continue on, but she probably thinks she's done nothing wrong, teenager's do have a habit of thinking the world revolves around them and no one else understands, it's a stereotype for a reason, but I think it's been made worse in this situation because her mum seems to be trying to be her friend rather than her parent.