Having read all of your posts, I don't think this is about the child.
I get a very strong vibe this is about you and only you. This teacher has taken against you for your non compliance of
his orders. Bully, misogynistic prick, over zealous, arrogant or whatever. Who knows for sure but there is something about his behaviour that says he's trying to stamp his authority over
you, determined to win a pissing contest over a detention.
He has been very disrespectful of your employments.
This teacher is saying the functions of his employment (as in doling out discipline in the form of detentions in this case) are to be adhered to and respected by you but your job is too unimportant to even require prompt attendance of if he deems it necessary to hold you up.
My money is on power tripping misogynistic prick but that's just my opinion.
Just because someone is a teacher, doesn't automatically make them a decent person. Most are wonderful people, of course, but not all. It is, unfortunately, a position open to abuse by power hungry aresholes. I know of plenty of good teachers who have their own battles with the staff's resident prick.
As for the posters who cannot comprehend living in a rural area that is a danger for a child alone in the dark with no lighting and not a soul around, give over, eh? I would not fancy walking alone down unlit country lanes on a dark winter's evening and I am nearly fifty with a twitchy ball kicking foot and a fine right hook. There's also the consideration of the fact OP states the roads are so pot holed that a taxi driver refuses to risk his motor getting damaged by driving down them. I'm not sure any of you would fancy lying in middle of a dark desolate country lane with a broken ankle in the middle of winter. To put that risk on a fourteen year old girl is not something many modern day parents would be comfortable with.