The best way to keep goats in one place is to use Heras fencing. The type building sites use. Best thing ever invented it is. I keep goats and poultry and my goatyar and poultry pens are made of the panels which are 12 feet long and 6 feet high.
I own 18 dogs which are 100% stock steady and luckily don't live in livestock farming country. If I did, I would make sure none of mine ever got out (they don't anyway) because how would a sheep or cattle farmer know that my massive 65kg of amiable dog isn't in the slightest bit interested in even chasing his livestock? I wouldn't want to risk one of my dogs g etting killed. I personally don't own a shotgun and don't think I could bring myself to kill someone's pet dog, however, if I had a problem, I might invest in a painball gun. Not only do they flipping hurt, but would make a real nasty painty mess of any dog. I would ask the newspapers to print a story saying that your dog gets paintballed the first time, but killed the next time.
Dog licences won't work. It'll mean that careful dog owners like me have to struggle to find the money because we care about our companions. Less caring owners will simply offload their dogs and as per usual, the scumbags just won't buy a licence and know that the law won't do anything about it. It is illegal to own a pitbull terrier type dog in this country yet I know of several pitbulls in my local town which the police do nothing about. The owners say that they are 'Irish staffordshires' or 'Amstaffs' which is just pitbull by another name.