I've been through the CHC system, on behalf of my elderly dad. I couldn't get much help from anyone so worked it all out myself, and ultimately had CHC awarded via appeal.
It's a gruelling process, to say the least.
You've mentioned that your mum would need 24/7 care from two carers. Do you mean two people would literally be required at all times? If she can't sit unaided, and cannot do anything for herself, what would those two people be doing on a minute by minute basis?
I'm not asking to be nosey or harsh, but to get CHC you have to show that the patient needs nursing care, so either they have complex medical issues and/ or extremely challenging behaviour.
My dad couldn't be left alone for a single minute because, as well as his physical problems, he had no concept of danger, was at risk of wandering, would frequently attack people, smash up his room etc etc. The Assessor decided this wasn't challenging enough and we were initially denied CHC.
The other issue is that someone can be awarded CHC but further down the line it can be removed. Not because the patient has miraculously recovered, but because they've become increasingly less mobile, or are now completely bed-bound, and ironically therefore deemed easier to care for.
Having said all that, from reading about CHC it can be very much a postcode lottery, some areas you're far more likely to be awarded it than others.
It's worth reading up on the National Framework, it might seem daunting but at least then you've an idea how the system is meant to work.