Yes, if they want it, they need to do it. I'm glad that they've agreed now.
And yes, they are expensive. That's what I have mostly gotten over the years.
It's difficult to get cats to leave, and not come back. Especially when there's such good hunting as there is there.
I hope that this cat will follow the dog house home, and hang out there more. Do they have a dog?
Love All Life, Thank You For Posting! :)