We have about 100 chickens or so, and 17 goats (7 full size Nubians and 10 pygmies/Nigerian dwarf goats). Our chickens have two coops, both outside of the goat enclosures. The full size and small goats have separate pastures (likewise the 3 Icelandic sheep). The chickens have feeders and waterers outside of the goat enclosures, but they spend much of their time inside the goat enclosures. We enclose our goats with cattle panels. The goats can't go through the welded wire panels but the chickens can. They go where they like. They pick and scratch around in the goat area a lot. They seem to like taking rides on goats backs. Sometimes the chickens roost on the goats' backs in the goat barn instead of going into the coop. Either way, they are all happy and cohabitate really well, but I agree that the chickens need a feeding area that the goats can't get to, otherwise the goats will eat everything.
As for pygmy goats protecting chickens from a bobcat...I'm not too sure. I think a bobcat could probably win against a pygmy goat, but don't take my word for it. We have llamas to protect our pygmy goats from foxes and coyotes.