Do you have boys or girls? It's probably just the age. My 3 yo little girl is ALL OVER the dog. He's just about 6 months old and the nipping has pretty much stopped, but a few months ago it was the same deal. All I heard was, "MOM!!!!!!!!!! Emmie bit me!". All the time.
I don't have great advice. I just kept pestering my daughter and Emmitt grew out of the nipping. Now when she has him in a headlock and puts her hands in his mouth he just sits there.