I am afraid this is all too familiar and lots of people seem to behave in a very similar way to your MIL. Is she not washing or showering at all? Is she incontinent at all? The CH may be prompting her but she is reacting in an aggressive way. Probably outraged that she should be reminded to keep herself clean, and probably thinks she is keeping herself clean. It's a horrible situation that so many people hate having personal care. Maybe the CH could step up and be a bit more hands on in her care, and take over the showering and bathing. I am sure she will be furious but they should have various approaches they can try if 'prompting' is not working.
Would she let you help her shower etc? She may be happier if a familiar person helped her. Worth a try though of course, not what you expect to have to do when she is already in a CH.