What a crap situation, for everyone
I only have interpersonal advice, that you are free to ignore!
Do you have a clear idea of the actions that need to be taken for C to remain in her home? You have sought advice and have been paying attention, which is admirable and sensible as this is your home too.
It is obvious that you give a shit about her so maybe you’d feel better about looking after yourself and moving forward if you write her a list of things she needs to do/people/orgs to talk to? Like, a numbered “1. Speak to X to find out Y. 2. Write to Z at PH including a copy of The Thing” list so you can start your planning with the clear knowledge that you’re not walking away from her and being sure you’ve done all you can. Email it too, so you can send it again. Perhaps C will reach a point here she can get her head around this and your list will be helpful.
I dunno. It’s hard to put oneself in C’s position as it’s fucking tragic, and of course she’s at a stage where everything is 100% overwhelming. So to think of yourself isn’t selfish or whatever. I personally love a list, but not everyone else does but maybe it's a small way ease any feelings of ‘washing your hands’. Looks like everyone agrees you should, but it doesn’t have to be without a second glance.
Hope this is even slightly appropriate! Good luck ☺