Cat ownership

So I have a situation, on my road there's a family that had 3-4 kids, a mother and father, all the kids have moved out over the years. The mother passed away leaving the father all alone in their home. All of a sudden their cat is at my back door meowing and wanting to come in, I notified the father on Facebook and no reply, I let the cat in, the cat doesn't want to leave all day, his just sniffing around checking everything out, I keep messaging but still no reply. The next day I go over to the house and his saying his too busy to talk and needs to go, hops in his car and drives off. I message again asking when he will take the cat back and he blocks me, so I just went along with it, let the cat stay, fed him and everything, the next week the youngest daughter came to my drive to pet the cat but once she saw me in the window she ran to her dad's house.

I took it as the cats mine now, he had the same collar on and his very unique so she obviously knew it was hers, there's no mistaking that.

I never got to find out the cats actual name and I thought it would be weird to name him as he was already an adult so the family call him kitty, my 2 kids absolutely love him and his now a part of the family.

4 years have gone by since kitty has been with us and the daughter I mentioned suddenly wants him back, says she's finally moved to a place where she's allowed pets and she misses her cat that I have now found out is named chico, says the kitty was a big part of her mother's life as he kept her company on the days the father worked.

I told her that I'm sorry but his now a part of my family, his an outdoor cat so he was free to leave anytime but he didn't, its like he chose us that day he came to my door.

She starts using abusive language and threatens me and my home, then says she will take me to court.

What do you guys think, what shall I do??

They had no contact with me whatsoever, never asked me to pet sit for 4 years and take care of him financially 🙄