It's not really either a behavioural or training problem - it's just perfectly normal puppy play. He does need to learn not to bite, but there are good ways and bad ways of teaching that.
Most likely he does it more with your wife and son because he is more confident about playing with them. Not surprisingly, "sterness" is scary for a baby puppy and if you're good at being "stern" then that actually means you're good at scaring him - so he's reserving more of his play for them. Unfortunately, that doesn't actually teach him the lesson he needs to learn.
What you need to understand about puppy biting is that it is natural and normal and it is the way in which puppies learn about how to moderate the strength of their bite. That is a supremely important (possibly the
most important) lesson in a dog's life, especially one that is going to be around children. So rather than being stern (which just averts the problem but doesn't teach), it's better to teach him in a way that he can understand that biting
hurts and he has to moderate the strength of his bite.
Nature gives young puppies those razor sharp teeth for a reason. So that it will
hurt when they bite with even the slightest pressure. What would happen with their littermates is that when a puppy bites another, the bitten pup would shriek in pain and refuse to play with the biter for a few minutes. The biter would continue to pester, of course, but over time would learn that when he bit too hard, nobody would play with him. He would thus gradually learn how to moderate the strength of his bite - to play more gently. Shortly after that, all the razor sharp little puppy teeth fall out and he gets his much blunter adult ones.
Now the reason that lesson is so important in a dog's life is that there *will* be times in his life that he has reason to tell another dog, a person, or a child to
back off. And he'll do that with body language (which people won't notice), then with a small growl (which people usually ignore or react to with anger), and then a warning nip. Now, if the dog understands bite inhibition and how to moderate the strength of his bite, that warning nip really will be just a nip. Nothing to get worked up about. But if the dog hasn't learnt about bite inhibition, that "nip" may be a full scale bite. See why it's so important?
Now, we people can't emulate dog behaviour and generally shouldn't try. But some things are universal. The way in which puppies learn to play nicely is the same way people do. We as children learn not to bash others with sticks too LOL We try it, they squeal and we get ostracised and nobody will play with us. So we learn not to hit other kids with sticks or to bite them, etc. If you want your pup to learn that lesson, then it is best to teach him the same way. Sterness may stop him biting, but it will *not* teach him how to use his mouth gently. He won't understand that it hurts or that human skin is fragile, he'll only understand that you get mad if he uses his mouth. So he might not use his mouth, and you'll be happy. But when the time comes in his life that he needs to give someone (dog or person) a warning nip, it may be a hard bite instead. So it's better to teach him properly while you have the opportunity
And the way to do that is the same as how human kids react to being bitten by other kids, and puppies by other puppies. You give a high pitched shriek of pain - "OUCH", and retire "wounded" from his game. Refuse to play with the biter for a few minutes, and ignore him completely. Reingage a couple of minutes later, but be prepared to squeal again as required. He won't learn in five minutes (try three or four weeks), but he will come to understand that when he puts any pressure into his bite at all that it hurts, and that you won't play with him if he hurts. He wants to play (that's what this is all about), so he will gradually learn to be more gentle. Then his razor sharp teeth will all fall out, and he'll get his blunt adult ones. But the lesson he learned about moderting his bite will stick with him for life.
If shrieking and ignoring isn't working (some pups are incredibly persistent), you can escalate your ignoring to getting up and leaving the room, leaving the pup isolated on his own for a few minutes. That's a pretty severe punishment for a puppy (isolation). A time out in a pen is another possibility. And there is always re-direction too - to a toy of his own to beat up as he chooses. But keep at it. He will learn eventually, and by this method will be learning the all-important lesson of bite inhibition. It's very much worth him knowing
