I didn't see my Dad's NH either,and have no clear recollection of how it was chosen or by who.He was discharged from hospital for rehab but never left.Thank goodness it has worked out.At the time my sister had recently died after a long struggle with cancer,for the previous my parents had staggered from crisis to crisis and I was literally at the point of breaking down.Terrible times.Sorry for the tangent, OP.
TooHard, I am sorry to hear my post resonated so much with you and that you face such a difficult situation with your mother. My description was actually a bit sanitized; my mother's home was filthy and horrible beyond belief. (It's difficult to imagine that dementia, or any disease, could affect one's brain and perception to the degree that living in dirty, unsafe, and miserable conditions, combined with constant anxiety and distress, could be interpreted as "fine." I really, really hate dementia.)
I have lots of sympathy to offer, and not much useful advice. Just two things:
1) if family is all at a distance from your mother, move her closer to the person with PoA, or the person who will be able to visit most, or just closer to someone. I moved my mother from 100 miles away to 10 miles away and it's been a huge relief, just to have the drive shortened.
2) if you are able, investigate care home options BEFORE you need them. You could even put her on some waiting lists; it's usually not a big deal to refuse a place if it becomes available, but remain on the list. I wish I'd had more time to look at care homes and that I hadn't had to do it in a hurry, stressed, and upset while she was in hospital. (One of my dirty little secrets is that I never saw the care home my mother moved into, until she moved in. I was 100 miles away with her in hospital and my husband is the one who picked out the care home here where we live. I normally don't even admit this on TP because it seems [insert judgemental word here], but it is what we did. All judgement aside, it was not a method I'd recommend.)
You have my sympathy. It is awful to know you have to wait for the crisis. I'm so sorry.