1). Our club has no policy re dogs that I am aware of, but no one brings one in the daytime mid season. Sometimes in early season, we might bring our dog and a tennis ball and walk a few holes. Others do too. There is a group of people (and the super) who meet each morning early....sunrise.....and run their dogs on the course, let them swim in the river, etc. it’s funny, most members don’t even know about this little group of about 6 dogs.
2) coyotes in the northeast are very large, part wolf, and very dangerous. We’ve culled lots from our course, and the super finds lots of little dog collars and dog parts when he finds a den. “Missing dog” signs everywhere. They go after the hamstrings to cripple, then attack. The “fake playing” is just that, an attempt to distract so another coyote can get the hamstrings. We trapped one that was near 100 lbs, they can be big. We don’t let our dogs out at night without turning on lights, making noise, etc.