UPDATE: Well, the dog was back again this evening. Not that anyone is surprised. Both Dear Wife and I were out in the yard watering plants, mowing grass, etc... So the dog knew we where there and did not go near the chicken coop or run. She was sneaky that way. But she was wandering around the yard, the house, and the garage. I walked her back home, again, but took a different approach this time....
Yeah, that's probably a good idea to put the scare into them. I did something similar this evening. My property boarders the highway, and I saw the dog up around the road, not on it, but close to it. Anyways, when I brought the dog back this time, I told them their dog was back in the yard, but saw my wife and me outside so it did not bother the chickens, but it was wandering around the highway and I was worried that she would get run over. The neighborhood has had a number of dogs that have been run over on the road, so I told them I hope they don't have to bury their dog before they go home.
I have considered taking out my air rifle and scaring off the dog with a BB pellet in the butt. But, really, the dog is very old, weak, and limps really bad. Probably been the family pet for about 13 years. I don't think I would have the heart to ping her with a BB to scare her off. I don't have any firearms anymore. So, shooting a dog, or any predator, is not an option.

My grandfather was a great outdoorsman and he had me out deer hunting before I was in kindergarten. I grew up with firearms like so many other boys my age. When I was in college, my grandfather was in the hospital from a heart attack, and someone broke into the house and stole all our firearms while we were visiting him. Unfortunately, it was a relative that had a drug and money problem that set it up. Not too hard to figure out, but, of course, the cops were clueless even given all the info we had. They said they could do nothing without more proof. Well, grandpa died, and none of the stolen goods, including all our firearms, were ever recovered. I never bought any more firearms because I mainly shared that experience with my grandfather, and those days were gone.
If I ever experience a predator attack, I may change my mind and buy a 12-gauge shotgun for livestock protection. I'm not at that point yet. I would not have a problem shooting a wild predator, but I am much more hesitant about taking down someone's family pet. Maybe I'm getting too soft in my old age?