The question is not if the dog will hunt, but is how to make the dog leave the cats alone.
Almost any domestic animal can learn short words which are consistently used for the same thing. They quickly learn “NO” or “NO NO”, especially if followed by a scolding if not obeyed. Dogs dread being scolded.
Scolding usually out does a cattle prod.
When your dog starts after the cats you must quickly intervene with a “NO NO” and a scolding. The dog is probably just wanting to play with the cats and the cats are reacting as if they are prey.
The pets will likely never become real good friends but they must all learn that you are family, the dog is family, the cats are family, and we all better learn to get along.
No people should have to fear the will of their government; all governments should have to fear the will of their people.