I think you have to accept that a teenager at home while the parents are at work, is a different thing than a teenager who is at home while an adult is in the house, where the adult is not granted any authority over the teen.
If I am away, whether at work or on holiday, and my DH decides to leave his kid at home alone, at whatever time of day or for any length of time, the kid still remains my DH's immediate responsibility. If something goes wrong, DH will have to sort it out and would, as well, be held liable for any consequences. If the kid needs anything he can't manage himself, he'll get in touch with DH for it, or do without
But if I am there, I am in loco parentis. I can hardly pretend not to see when the kid does something unsafe or illegal or damages something in the home. If something did happen, I'd also be the one who would be blamed - by the mum, by the legal system, by the parents of teen friends if they were involved, by the collective of mumsnet...
I've not said that the child should not be there - but I do think it is absurd to suggest, as some have, that the OP will not be affected by her presence or that she should not have any say in how the situation is managed.
I also object, on a separate point, to the inconsistency on these boards regarding the parenting of teenagers.