Your daughter was 15 at the time, she had the correct ticket, she was doing nothing wrong - fair play to her for refusing to provide her name and address to a male proporting to work for a TOC (it’s been known for people to pretend to be railway officials before).
There is no requirement to carry ID in this country, it would be easier to do so if you wish to buy age restricted items of course.
Let the official kick up, make a scene or call the police (good luck getting BTP to attend), no guard in their right mind will eject a 15 (suspected 15+) female from the train alone - if they attempt to simply refuse to move, again the majority of other passengers will support the lone female.
Bad day or not this is the type of person who really shouldn’t be in the role anymore, they’ll come across someone equally as obnoxious at some point then moan with attached “compo face” when they get a punch in the face.
Treat people how you wish to be treated.
Signed, a ex guard.