Well, I understand about family situations.. it can get crazy. On one hand, I like the trap idea, trap the dog and call the dog warden to come get it etc.
I agree with some of what has been said about another dog, it can just add to the problem... BUT, IF (and that can be a very BIG if) you get the right dog, it CAN work.
I had an Australian Shepherd/Border Collie mix that was perfect as far as he only herded the hens off of the edge of the road which he (rightfully) considered unsafe for them, and also, would tolerate NO OTHER DOG AT ALL on our property!! No dogs, no coyotes, raccoons were unheard of, and possums were rare and usually treed! (though that isn't in an Aussie/BC's resume normally) Trips to the vet were a fact of life with him, shots were a MUST!!!! 'cause raccoons can be VERY dangerous if big enough, other dogs, including a marauding pit bull was chased off with its tail between its legs, yipping in pain, but I had to pay the vet for the stitches for my boyo that day. I questioned if it was fair to my lad who would have given his life that day protecting his charges... well, it was his job and he was PROUD of what he did!!!
He would only very gently press the goats towards the barn, he seemed to know that they needed very little control where they were, and when I took him to work cows at a larger farm, he could go out and bring the cows in all by himself because he was so mellow. Milk cows need little actual herding after all, just a little 'notice' and gentle nudging that it's time to come in.
I really don't know how he would have handled a challenging herd of sheep that would have pushed him and his mellow ways, maybe not too well. He was taught with his mom on some pretty tough cows... but, pushing sheep where they don't want to go might have been too much for him. I want to say he would have risen to the challenge, and he could flank with another dog very well, but... I'll never know cause he's long dead now. What a good dog he was though.
I digress though, getting a dog already trained would be expensive and getting a puppy would take a long time, so, I think a trap and a phone call to the dog warden sounds smartest for now.
Not all land is conducive to fencing, (very hilly and wooded here) not secure enough to keep dogs out anyway, I couldn't watch my chickens when I let them out either, and not all dogs should be expected to be trustworthy or trainable enough to work out as guards for your livestock.
A combination of solutions, and some long term plans seem to be in order. A secure run for your hens for now, a carefully selected dog of your own, trained as a herding dog or as a livestock guard dog, (neither of which is simple OR cheap), SOME fencing to at least deliniate your property,,, that dog might actually respect a boxwire border-line, I've seen stranger things (but wouldn't count on it)... and immediate control for the current problem with traps or a shotgun loaded with rocksalt or non-lethal shot if you wish, or actually sss'ing that dog, but, not sure I recomend it myself, though it is an option.
