The only predators I have to worry about are my dogs. We have our coop and run built inside a chain link fence. My dog would go after them if you gave her a chance. She will watch them like she wants to pounce on them. She is a black lab! I can't let my chickens free roam because of her. She is a inside/outside dog, and I would be so scared that she would get them. I don't have to worry about anything from the skies because we have chicken wire over the top of our run.
You need to a handle on this. If you are the pack leader of your house your dog should respect your wishes. It is not a democracy.