I wonder if the op has sorted this problem yet.
I'm with bluerussian about doing own laundry. It used to be the thing that when girls started periods (or just before), they'd be taught to do it, get blood stains out with cold water etc., not save them up for days to go in the washing machine. It doesn't have to be at night, not everyone has a bath or shower at night, could be in the morning if there is time (or midday at weekends!).
It does seem old fashioned to some I suppose but I tend to still do it, but I am a lot older than many on here.
Another thing which I know people do is give their kids wash bags, netty things, to put their own stuff in to go in the machine. Separating whites, darks and lights. That's not a bad idea. They do that in boarding schools so washing doesn't get mixed up with other people's. I boarded for a while and our clothes were sent to a central laundry but we all washed our pants and sox or tights every night and put them on pipes and radiators :-). Those were the days (we were lucky to have pipes and radiators, it was still bloody cold). We each had a number on our clothes done with a marker so no-one would put on someone else's stuff.
At fifteen the girl shouldn't be expecting mum or anyone else to wash their bits and pieces. I think she would like to do it herself, it's probably just not occurred to her.
Good luck op, hope things are improving on that score.