Why is mom on your couch? Why is she allowed to have multiple cats? Why are these cats not getting veterinary care? I encourage you to speak up and say no to these things and take control of the situation. I also would get her to see a doctor - even a GP will be a start.

Collecting animals is a type of hoarding. Not to mention having cats that aren't getting veterinary care is health risk to the humans in the home. She needs help - and a family doctor is a good place to start.