It's difficult to say. This is from my experience applying for my father. It's not just about needing a lot of care, they look at whether it's unpredictable and complex. They say it's whether her primary need is nursing as opposed to "social" - feeding, incontinence, washing all are social. Turning at night to avoid bedsores isn't enough, but the underlying need, the need to take care of the skin and make decisions on day to day treatment is on the nursing side. If her condition is stable and just needs people to carry out the same activities every day, you're less likely to get it, if there is a need for a medical decision every day, you're more likely to get it.
The first stage is a quick questionnaire to filter out the no-hopers. If you get through that, your chance of CHC is still low. You can download the second stage application form and see what they're asking about. Google CHC framework tool.
If you don't get it, you should still be able to get the "nursing contribution" which is about £100 a week, and paid direct to the nursing home if that's where she is. But the home may assume you'll get that, and the fees quoted to you will take that into account -ie if you do get it, it won't make any difference to what you pay the home. I don't know whether you can get it if she's at home with carer support.
If she is at home; or if she is in a nursing home and entirely self-funded (no LA contribution), she should get Attendance Allowance at the higher rate, about £80 a week, not means tested. But she'll only get that if she's paying the full fees herself.
You say "The cost to the family of meeting these needs is alarming." If you mean financial cost, that should all fall on your MIL. And the LA will take over when her savings run out. So it's important never to understate her needs when talking to Social Services - there needs to be no doubt in their minds that she needs a high level of care, and a nursing home rather than a care home. My experience is that caring for her at home will be difficult as social services carers don't work at night. So you either have to do the night time turning yourself or pay for someone to do it, whereas in a nursing home she would get that night time care.