Hi Calmgirl,
As a mother I feel your pain. As a daughter I feel your continued "interference". But you are in torment, and need to find a way to turn.
I would suggest you stop looking for blame. It's irrelevant. The fact is, your daughter's struggling with her mental health, and for whatever reason thinks it might be easier to go through this without you. Without your help, or your analysis, or your whatever you usually do.
So until you can stop doing those things, she's going to need to keep you at arm's length. If you want to make it easier for her, stand back and don't make her have to push.
And perhaps realise how lucky you are. Your daughter sent you a No Contact letter. Many are just left to work it out!!
Think about what you actually need right now. If one of the siblings or grandfather will let you know if the worst happens, then stop pushing for more.
Meanwhile, you have a perfect opportunity. "Is there any thing she needs?" She's in hospital! She needs a pack of new knickers, a pair of cool summer pyjamas/loungewear, a hairbrush, a toothbrush, and a good book. Ideally give the money for these to a sibling/grandfather to buy and drop off.
(If you get them yourself she'll recognise your taste and they'll be a pressure instead of a pressie.) If they question, you can point out that she did send Christmas gifts, so hopefully this doesn't infringe her NC "rules".
Leave it at that for now. If she responds in any way great. If not, that's up to her.
Meanwhile, Please note: you cannot promise her that "things will get better". And it isn't for you to give her the benefit of the doubt!
And finally, go and do a module of your Masters in Psych. Or write an extended essay. Or something. You need to concentrate on something that will absorb your attention, so you can leave your daughter in peace while she works on getting through this situation and, hopefully, getting a little better.
I wish you well, take care, and TAKE A STEP AWAY,