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This is 2-sided answer.

If the dog is still in puppy mode and wants to play, then when it starts nipping, have the kids tell you right away. Go to the dog and give it a correction. One thing that you can do too with any aged child is, take their finger and put it in the dogs’ mouth. Have the child say in a high pitch voice,  “OUCH!” Don’t remove the finger, let the dog remove its’ mouth. This will teach the dog that “ouch” is the equivalent to when the dog says it in their language.

If it is an older dog in the house, the dog may actually be telling the children to calm down, and may use its voice in barking, or mouth by nipping. Acknowledge the dog for this.