Well done for getting her seen again and being persistent enough to get a diagnosis.
If you feel up to it, will you write and give feedback / make a complaint?
It doesn’t have to be a huge one, but I do think that doctors sometimes carry on convinced they are right as they don’t ever get the feedback that would make them reassess their behaviour and develop as a doctor.
This doctor was dismissive and had decided you were whining and nothing was wrong probably based on assumptions and stereotypes
For example, perhaps he decided that teenage girls do faint / exaggerate or whatever. Plus over protective parents see things that aren’t there... or perhaps he decided that patients often add two and two together and make five.
Whatever his thinking, he didn’t bother to take your DD’s symptoms seriously. He didn’t appear to focus long enough to work out a really quite basic thing - why the severe non weight bearing leg pain could possibly be related to a girl fainting... err, from the pain!
He also sounded like he’d judged you based on his incorrect assumptions and decided he could be quite rude in dismissing your dd’s symptoms, and being clear how annoying and pointless your visit to A&E was...
So, lots of reasons why he might have made that error in judgement, and not necessary to haul him over hot coals (maybe?!). It was hard to spot, he was probably tired, over stretched, had more life threatening patients to focus on etc etc etc...
But without being informed that he actually made a wrong call that evening, your interaction will have actually strengthened his views and he will likely treat others the same way in the future.