This is a most heartbreaking, truth-filled account of what it's like to live with a hoarder. So well written. My sister who died of vascular dementia a year ago was a hoarder, though not as serious as your mother, (as if degree matters. I don't think it does). She had to be moved to a care facility and the family had to trick her, take her out to lunch, then back the dumpster into the driveway and empty the place.
It's a mental disorder, in my humble opinion. I'm actually writing a piece about hoarding and most professionals assess it as a form of OCD. But also a disorder of the heart, because most hoarders are actually very loving, emotional people. (My sister was)
Blessings, I'm relieved to know that you have such a great relationship with your mom. I do wish though that those cats could be neutered and treated, I'm sure they're all sickly. My gosh. Please reach out to a rescue organization who may be able to help.