I have not heard specifically of any issues of having cats around even though they have been known to transfer some viruses and diseases to people. I have two dogs and I believe my two teenagers are a bit more unsanitary than the dogs

. If you mother is close to the cat, it may do her good to have her pet around her. I made it a point to keep the kitchen and bathrooms extra clean and changed the sheets often when the blood counts were low.
Most of the anti-nausea meds made me tired, too, and I sure tried enough of them. I went with suppositories, too, since I couldn't keep anything down.
Things will get rough for a period of time but they will improve. As Gary says, it is very hard on the caregiver especially. Hang in there.
Ed