My nursing home is owned by one of the hospitals in town, which happens to use pet therapy thats where our pets come from. I would see if the hospitals around you have pets. Plus we own a dog and a cat, they both live at the nursing home might want to see if you can go that way.
I have had the same problem except it was the Staff spreading it. I went to the social worker and administor about it. They took care of it quickly, i would talk to the social worker, at my faucilty she has taken care of the gossip between residents spreading rumors on each other.