Up here we have some large coyotes, the results of cross breeding with wolves and domestic dogs. They have little fear of humans. I have a fairly large pack living in the woods behind my house....up to 6 or 7 at a time, more when the cubs come out of the den and learn the fine art of being a coyote.
They have paraded between my house and garage, in a narrow walkway of 5 feet wide. They also used to sit in the horse pasture at night and howl. The pasture is my back yard, as I only own an acre.
My Malamutes keep them at bay now. The coyotes howl and are answered by my much larger Malamutes. As soon as the Mals howl in answer to the yotes, the yotes high tail it out of there.
Your idea of fencing around the chicken area with your goat fence and letting the dog guard the area is a good one. I am getting a Pyr pup soon and that is my plan. The new goat barn will be next to the chicken area. The goat pasture will be built with the chicken pens in the middle, so the dog will be able to protect the chickens and the goats at the same time.