16 year old rejects autism diagnosis

It sounds like you’ve both had such a challenging time - I’m sorry that life has been so difficult for your family recently. That’s a huge amount to cope with. Your daughter is probably feeling traumatised by her recent stay in hospital - that must have been very distressing for her. You must all be dealing with so many difficult emotions right now - and it’s understandable that life is feeling completely overwhelming for her right now. 
If your daughter - at this point in time - feels that the autism diagnosis is not helpful for her then I would focus much less on that now. It’s only useful if it’s useful - and helpful. If it’s actually upsetting her now then I think it would be a good idea to ‘go back to basics’ - let go of definitions and labels and just focus on deeply listening to your daughter and focusing on what WOULD be helpful to her now. At this point that might be - for example - not talking about her problems or her diagnosis. But the point is : focus on helping your daughter know that you are there to listen to her - truly listen deeply - and support her in whatever way SHE feels she needs. Not what the doctor says, or the therapist, or the diagnosis suggests - but what she truly needs right now to feel better. 
It sounds like she is being very hard on herself. Do all you can to help her see how essential it is that she be kind to herself. She is only 16 and frankly being a bit of mess at 16 is entirely normal and if she can be more forgiving of herself that would be a huge step forward. Maybe she is panicking that if her life feels like a mess now then it will always be that way - but most of us when we look back to our teenage lives realise that our feelings of overwhelm at that age were actually not as unusual as we felt them to be at the time. She will get through this - there is a life beyond the intensity and suffering that she is currently experiencing- ‘this too shall pass’. 
What does she enjoy doing? Maybe try to shift the focus away from all her problems and the diagnosis and more towards cultivating happiness and doing what she enjoys? Sometimes all the focus from people like CAMHS etc can make children feel that the main focus of their life is all their problems, leading them to feel broken and hopeless. Try to help her to focus on other things for a while - the things she enjoys - even if they are trivial or frivolous- it doesn’t really matter what - the important thing is that she has a break from all the intensity of her health issues. 

Yes, this was my thinking to begin with, right from 2022, however, she will not engage with anything and no longer enjoys doing anything and refuses to do things she has previously enjoyed such as drama, creative tasks etc. She is totally isolated with no friends. She has never shared that she doesn't eat with anyone and she has not been able to have food or drink without us in 2.5 years which obviously limits her ability to live freely. 

She does not know who she is, or what she enjoys, and as a therapist myself, whilst this is normal for most teenagers as they explore their identity and grow, she is almost frozen in time for herself. This year she has developed a total reluctance to leave the house unless for something she doesn't want to do (appointments, exams, school) but not for things she might enjoy (trips out, theatre, she refuses to watch any tv/films, read etc) which fit the self punishing aspects of her experience with ED and rule following. The thinking for her therapists and psychiatrists alike, was that a diagnosis would help her to begin to make sense of her world and build her identity.

The therapist she has had has been very hands off and tried to focus on what she needs right from early days because it was evident she was struggling with communication. However, she is unable to communicate how she feels and is so compliant that leads to lots of inner tension within herself which she turns on herself rather than the outside world, or us. She is exhausted.

I wish I could help her to focus on things she would enjoy, and have been off work since February to support her and offer a space for her to do whatever she needs, but she is not able to do this at present. She has strict rules about what she does in a day and it involves, eating at certain times (the exact same food daily or meal replacement drinks), listening to podcasts and having a shower. She is cocooning for now I think after a very difficult few years and hopefully she will have space to do this when she feels able.

My guess, and it is only a guess, I am not qualified, other views are available etc., is she is controlling what she can control, e.g. food and routines, because there are other things she is scared of, or embarrassed or confused about that she cannot talk about or control.

She is going along with the things she does not like because it is a duty. But optional things, like things she likes, she wants to avoid. She is maybe on autopilot.

She could be traumatised from feeding and/or depressed. If depressed she may not know what she likes.

She probably wants to be left alone. I would.

The anger may because she is the focus of attention. She may also view it negatively because she still thinks or wants or dreams of being the same as other people, and doesn't want someone saying she isn't. I would have been the same.

How to make things better is hard. Probably space, being left alone, maybe ask her to write how she feels or what is bothering her. It is easier to write. Make sure she can do this in private, and maybe share the odd point when she is happy. Don't try and sneak a peek, it is her secret. Maybe give her a locked box to keep her notes in.

Build trust and let her know she can share something when she is ready. There is no shame and you won't judge. She won't believe you but you might get a gap in the armour.

I was always too scared to tell people what I really thought, till I got to 56. Maybe she can do it without waiting 40 more years.

My guess, and it is only a guess, I am not qualified, other views are available etc., is she is controlling what she can control, e.g. food and routines, because there are other things she is scared of, or embarrassed or confused about that she cannot talk about or control.

She is going along with the things she does not like because it is a duty. But optional things, like things she likes, she wants to avoid. She is maybe on autopilot.

She could be traumatised from feeding and/or depressed. If depressed she may not know what she likes.

She probably wants to be left alone. I would.

The anger may because she is the focus of attention. She may also view it negatively because she still thinks or wants or dreams of being the same as other people, and doesn't want someone saying she isn't. I would have been the same.

How to make things better is hard. Probably space, being left alone, maybe ask her to write how she feels or what is bothering her. It is easier to write. Make sure she can do this in private, and maybe share the odd point when she is happy. Don't try and sneak a peek, it is her secret. Maybe give her a locked box to keep her notes in.

Build trust and let her know she can share something when she is ready. There is no shame and you won't judge. She won't believe you but you might get a gap in the armour.

I was always too scared to tell people what I really thought, till I got to 56. Maybe she can do it without waiting 40 more years.