Worst Cat Ever

"Dogs hide when they have done something wrong. Cats are proud of it." - Internet Meme

From the very first stormy night that the black feral tomcat arrives at our home he causes trouble. He continuously teases the family pet, a cocker spaniel/pug mix named Brandy and quickly figures out how to trick Brandy into getting punished.

Youngest daughter, Bean, names the cat Goblin and, true to his name, he spends his time plotting how he can torment the one person in the family who doesn't like him.

Even after being shood away, the cat comes back. Every time he's let loose to hunt, he returns with a trophy. The trouble is that he always returns.

Is there any way to rid a family of a cat that doesn't want to leave?