missiondecision lovely that so many people want you to allow your anxious, young for her age, 17 year old daughter to be put in this position!
I certainly would not be allowing or encouraging my dd to go at age 17.
I think you should like a caring mum and rightly concerned.
"I feel shit with everyone saying I can't stop her. I know I can't." You can continue explain your concerns and allow her to know that it is not because you want to stop her fun.
I'd talk to dd to see if she actually wants to go. Parties can be quite boring and actually for a socially anxious person who knows no one at the party it sounds like a fucking nightmare! It may end up with her drinking too much due to boredom!
If she really, really wants to go just say you will collect her a couple of hours later. "..she was not happy about picked up by her parents." BUT No one would know how she was getting home except her friend. You could call her, say I am a few doors down, she says bye to her friend, leaves party and gets into your car."
Personally, I would not let her stay in an apartment of a man of twenty where there are likely to be several other drunk men. And i would not allow her to travel back by train at night alone. She may be very grown up at 17 (although you say she is not) but she is still a child and lives with you.
If she, at 17, sneaked out and did that, it is her choice and, I feel a poor one.
Get her views first, why does she want to go, is it just to prove to her friend she is 'grown up' - what pressure is her friend putting on her?
Continue to explain your concerns.
Her friend sounds like a bad influence friend. I had one of those years ago, wanted me to go on holiday at 16 with her and her older boyfriend and his friend and sleep with his friend (so I found out in time and did not go).