Take it to the dog whisperer- if he can’t fix the problem, noone can. If you can’t take it there, I wonder if there is a forum of his where it can be asked if it’s possible to train dog not to do that? Or maybe an internet search for “Train dog not to kill cats” might have some advice?
We had a Sheppard once that turned ugly and wouod kill other dogs. It was given to a junk yard in the end I beleive. Maybe that might be an option?
I had a dog that kept killing my chickens.
I know it sounds cruel, but it worked, I duct taped the dead chicken to the side of its head for the day. After that it avoided chickens!