Keep a toy on you at all times. If he bites, divert his attention. Don't give it to him right away, or he'll think that biting you is how to ask for playtime. But squeak it (if is squeaks) and wiggle it around, just generally make it as exciting as possible. Once he lets go, say "yes!" or "good!" (if you're a clicker person, click) and play with him for a minute. Redirection of his natural biting instinct is one of your best tools.
You said you did positive reinforcement- if that's jut treats, I'd recommend switching to toys, because the biting is a game to him, you want to show him a more acceptable way to play. (even in general training, toys are a very underestimated reinforcement tool)
Have your kids interact with him mostly just after he's been exercised. If he tends to be riled up after exercise, wait for him to calm down first. This is also the ideal time to do training with him.
**Try teaching him to greet properly first- instead of reacting when it does happen, try to prevent it.
-One drill could be you keep the dog on a leash while someone else enters the room. Ask the dog to sit, and if he sits, the other person can say hi to him: play with him, pet him, give him a treat, etc. If he begins to bite, the other person exits the room or goes out of his reach (since he's on a leash). Then you ask him to sit, and the whole thing repeats. As a general rule, if he's not actively biting- it's a puppy party: playing games getting pet, etc. Once he bites, though, everything stops. You take the toy away, stop petting him, and say "nope" in a bored voice. Once he stops, the party resumes.
-Another good drill is to close him in a room and open the door a bit. Just an inch or two. Wait for him to calm down, then open it slowly a bit more. Reach through to pet him. if he starts to bite, close the door again(but slowly. First of all, you don't want to hurt him by closing the door on his nose or paw, secondly, the quick movement would add to his excitement). Start all over. Reward him with play and pets any time he allows you to say hi without biting. You could also do a variation of this by leaning over a puppy gate. Biting=you leave.
-You could probably make up more of your own drills, too.
Try to get your kids in on these. Having the ability to be safe (closing the door, leaving the room) will give them a better opportunity to interact with him.
You said he gets plenty of exercise- great!
Have you tried mental exercise/stimulation? For instance, teach him a trick or two, do basic find the treats (scentwork), try a puzzle toy, and be sure to let him smell a lot on walks.
Whenever you can't be working with him you will need to keep him either fenced off by a puppy gate, in a playpen, in a crate, or on a leash. Biting is like a game, so it's very self-rewarding. The more he gets a chance to do it, the more he'll continue to do it.
In regards to saying leave it, since the puppy can't (of course) really understand what that means, it'll only work if you've done some serious training on that command.
If, when he bites, you tend to jerk your hand back (the natural reaction, I know) try not to. (you may need to wear gloves when handling him at first) When you jerk your hand away, it becomes a fun, moving toy. When you train "let go" with tug-of-war, you make the toy "dead" and boring-perfectly still- and then praise him the second he lets go (which he will, eventually, because he'll get bored). It's the same exact thing with hand biting, although that's harder to do for the human.
The general rule of thumb is, teach him that biting equals totally boring human who basically becomes dead. NO reaction, not looking at him, VERY boring. Not biting equals PARTY TIME.
You'll definitely need to do training sessions that you set up(primary sessions), not just training him whenever the behavior starts(secondary sessions).
If none of this works, you may need to consult a professional trainer and/or vet. Muzzling may stop the behavior, but it isn't a long-term solution.
You said you did positive reinforcement- if that's jut treats, I'd recommend switching to toys, because the biting is a game to him, you want to show him a more acceptable way to play. (even in general training, toys are a very underestimated reinforcement tool)
Have your kids interact with him mostly just after he's been exercised. If he tends to be riled up after exercise, wait for him to calm down first. This is also the ideal time to do training with him.
**Try teaching him to greet properly first- instead of reacting when it does happen, try to prevent it.
-One drill could be you keep the dog on a leash while someone else enters the room. Ask the dog to sit, and if he sits, the other person can say hi to him: play with him, pet him, give him a treat, etc. If he begins to bite, the other person exits the room or goes out of his reach (since he's on a leash). Then you ask him to sit, and the whole thing repeats. As a general rule, if he's not actively biting- it's a puppy party: playing games getting pet, etc. Once he bites, though, everything stops. You take the toy away, stop petting him, and say "nope" in a bored voice. Once he stops, the party resumes.
-Another good drill is to close him in a room and open the door a bit. Just an inch or two. Wait for him to calm down, then open it slowly a bit more. Reach through to pet him. if he starts to bite, close the door again(but slowly. First of all, you don't want to hurt him by closing the door on his nose or paw, secondly, the quick movement would add to his excitement). Start all over. Reward him with play and pets any time he allows you to say hi without biting. You could also do a variation of this by leaning over a puppy gate. Biting=you leave.
-You could probably make up more of your own drills, too.
Try to get your kids in on these. Having the ability to be safe (closing the door, leaving the room) will give them a better opportunity to interact with him.
You said he gets plenty of exercise- great!
Whenever you can't be working with him you will need to keep him either fenced off by a puppy gate, in a playpen, in a crate, or on a leash. Biting is like a game, so it's very self-rewarding. The more he gets a chance to do it, the more he'll continue to do it.
In regards to saying leave it, since the puppy can't (of course) really understand what that means, it'll only work if you've done some serious training on that command.
If, when he bites, you tend to jerk your hand back (the natural reaction, I know) try not to. (you may need to wear gloves when handling him at first) When you jerk your hand away, it becomes a fun, moving toy. When you train "let go" with tug-of-war, you make the toy "dead" and boring-perfectly still- and then praise him the second he lets go (which he will, eventually, because he'll get bored). It's the same exact thing with hand biting, although that's harder to do for the human.
The general rule of thumb is, teach him that biting equals totally boring human who basically becomes dead. NO reaction, not looking at him, VERY boring. Not biting equals PARTY TIME.
You'll definitely need to do training sessions that you set up(primary sessions), not just training him whenever the behavior starts(secondary sessions).
If none of this works, you may need to consult a professional trainer and/or vet. Muzzling may stop the behavior, but it isn't a long-term solution.