I'm not sure why your friend would drive for longer taking you to the station, than picking you up, it doesn't make sense.
Is it 20 mins, 25 mins ish 28 mins ish? etc. Does she come to yours and your not ready? Are there other occasions you could remember if she seems fed up picking you up & taking you home. Do you think she might feel, she pays for more things when you're out etc. Could she feel this is a one side friendship and she does more for you, than you do her? Do you give her £10 each way, or £10 total, Her house - to yours and return back to her house, then again in the morning will cost more than £10. Is she struggling financially and feels you might be taking the mick with your £10 offering?
There clearly is a reason, she's knows you have to catch 2 trains and she knows you have a wait between trains.
You write you worry you might pass out with palpitations/anxiety with no sleep, catching the train, or you might feel ill! This does sound very dramatic. Anxious or not. Are you usually this dramatic? It's a night out with your friend and a one off sleeping on her sofa!
She might simply be a bit fed up, of her going out of her way, additional costs in doing so. It also means she's leaving her children for at least 40-50 mins to collect you, then leaving them to go out, then leaving them again in the morning for 40-50 mins and it's simply easier for her, on this occasion for you to catch the train.
Have you thought at all about any of that?