@jasminajasminda
Your daughter was perfectly entitled to keep her seat. How dare the woman think she should be entitled to take someone's seat, and a young person refusing to give it up is 'in the wrong...?!' For all that woman knew, your daughter could have had a disability, or a condition that made it hard for her to stand for long periods.
Me and my kids have given up our train seats for people before - elderly, pregnant, and a woman with a toddler who was standing in the aisle with the child in her arms.... But on every occasion, we have had 20-30 minutes or so to go on our journey. (And we were all able bodied and fit...) No way though, would we have given up the seats if we had had a 4-5 hour train journey.
The woman in question needs to think ahead next time, and book herself a bloody seat, and yeah, the poster was right (on page 1) that the other people tutting and huffing and puffing, could have easily given up their seats!
OP, your daughter did nothing wrong. Good for her for standing her ground, and not being bullied by entitled middle aged people who think they have the right to treat a young person like shit, and the young person must be in the wrong JUST because they are a generation older than them!
To the people saying the OP's daughter was rude and mean etc..... why?
WHY was she rude and mean? She did not have to give up her seat, she did NOT have to engage any further, the woman COULD have asked other people - but didn't, and she was only middle-aged - not OLD. And no, the girl DIDN'T have to go and 'find the guard' for the woman, and she is NOT a bad person for not doing so! Christ-on-a-bike, there are some cheeky fucking 'entitled' individuals on this thread! 
I agree wholeheartedly with the posters saying she picked on a teen girl because she thought she could be bullied. She was wrong, and as I said, good for the girl for not allowing it to happen, and ignoring this rude woman.
@Stirner
The people that are saying they would be "ashamed" if their kids did the same need to take a long hard look at their priorities.
If you teach your children to roll over like that you're setting them up for a life of being tread on by others at the best. This is especially true if you have daughters.
This! Shame on the posters for saying the OP should be ashamed of her daughter. I salute the strong assertive young woman, who refused to be bullied by a middle aged woman. GOOD FOR HER!