As you found out lots of people are idiots. When it becomes inconvenient to be dog owner because of the dog's behavior, there are people who want to do the most convenient thing for themselves.
Unfortunately its the dog that suffers.
We had a rescue dog that was very protective of my children and family. You never knew when he was going to bite a stranger. He was a selective biter. He was great with the family and never attempted to bite us. This behavior did not make him a bad dog, it only made him a dog with a bad behavior.
Since we knew the dog had no health issues, we took some responsible steps with him. In an attempt to socialize him, we took him camping and walked him with a muzzle when he was around other people. Even so we still could not be certain that his behavior was modified, so we took the next responsible step and secured the dog when we had company in our home. This method was not only responsible, but protected dog and human alike. That dog ended up living a long and happy life in our care. He was a much loved member of our family until his passing over two years ago.
If the dog is nipping and not attempting to break skin, then its possible that this dog is attempting to get these children to play with him. This is typical of many dogs. Its how dogs play with one another, and it may be this dog does not understand the difference between children and other dogs.
Has that other poster in the other forum who owns the dog, attempted to have a child walk the dog, under adult supervision, on a leash? This would be a good place to start.
How much exercise does this dog get? Visla's have lots of energy and are hunting dogs. They need to run and get plenty of exercise. There are many times a dog can and will act up if they do not have an outlet for their energy. I suspect that if this owner is so inclined to easily put this dog down, then more than likely this dog is not getting the attention or exercise it needs.
New people in the house or on his territory will certainly get this dog excited and curious. I certainly cannot fault a dog for being a dog. You might suggest some obedience classes or consulting a behavior therapist. I wonder if the owner of this dog will also see that as an inconvenience.
Jason