From your posts op it sounds as though the ward environment was not particularly favoyrable for or sympathetic to her. I think she is oribably better at home but if you are not able to be there with her when she is not at the day hospital/centre then I think, at least for this week you need to be and to make sure you are.
You know your dd best and what will help her and you must be her greatest advocate. May I suggest that you spend the time this week revieeing the MH Act, The Capacity Act, Dols legislation and the Mind and Young Minds websites. It may also be helpful to get advice from yoyr local Healthwatch. Scrutinise too the MH Trust's website and request for yoyrself a carer's assessment.
Write to the Trust aboyt why you wanted her discharged, ie, the fact that the envuronment was not cognizant if her autism and ask for a meeting about her transfer of teams and care plan miving forward. Send it recorded so they can't lise it - in fact record everything they say they will do after meetings/apts and affrm with them - ime goalpists change.
For all that's been said on here, if she had been 17 still she'd have gone up to paeds for the night and would have been assessed the following day by camhs when she'd calmed down a bit and there'd have been no question of her refusing the nac CAMHS would havecsent her home with an oral care plan, possibly a bit of therapy delivered late, might have called her a few times and she would probably have said I'm fine to get them off the phone and that would have been that.
Get Healthwatch to help you with the care plan/transfer. It sounds as though she needs tailored support to help her manage her autism which shd impact the depression/anxiety/hopelessness.
I'm not an expert op but my dd was ill due to undiagnosed adhd - diagnosed at 17. NHS services were totally unacceptable and it wasn't all about funding, much of it was about competence and poor management. If you can't pay then you must learn to deal with the system and fight her corner.
You are her mum. You know when an environment is not helping her but you will have to be her squeaky whee and fight for her because nothing within the system will. You have her best interests at heart Good luck.