Pets do react to the stress in the house. Since Lorelei's family has been dealing with her illness for so long, maybe Kitty needs a foster home for a while, and to be seen by a Vet. Between being in a stable calm home, and being treated for her medical issues, hopefully she'll recover.

I know Lorelei's family loves Kitty, but she is a living creature that needs love and attention too, and if the family can't manage that because Lorelei is taking all their energy, then Kitty deserves a new home. It is a sad conundrum.