Question for dog trainers?

The dog is biting because of the pain. This is more of an instinctive act then a cognitive one. He nips without thinking because it hurts. Just like an older sleeping dog might bite when suddenly startled from a deep sleep. Sadly there most likely isn't much you can do to stop this except management. Biting him on the neck might get you a bite in the face in return. I certainly would not recommend that. Sounds like he is already pretty tolerant. Many painful dogs would do much more then nip. I've talk to the vet about doing some serious pain management on this guy. In the meantime separate him from the children.