This is a matter of not only training the pup, but the kids, too. Right now, your dog is viewing the kids as his litter mates. The kids feed in to this with the running, jumping on tables and squealing.
Your kids will need to, for the time being, tone things down around the dog. It's hard, especially when they are as young as they are. But it can be done. They also need to become actively involved in the obedience training. Even a 10 minute session (for each boy) with them working on sit, stay, heel (while you are supervising of course) will help them gain confidence around the dog and help the dog realize that the boys are to be respected as much as the adults. As everyone progresses and the dog matures, you might want to look in to agility training with the boys as his coaches.
In the meantime, it's imperative that you start reacclimating the boys and the dog. Allow them to spend time in the same room together. If the puppy nips (and at 10 months he is still very much a puppy), remove him immediately and briefly (5 minutes max) and then start again. No yelling, no hitting, no punishing. He needs to learn that aggressive behavior gets him isolated. If you wait to remove him or keep him separated longer than a couple of minutes, I guarantee he will forget why he got removed.
Think back to June. What changed at that time? What set all this off? Did the kids get put of school? Did you change something else in your household? Summer vacations and a lack of routines can wreck havoc on a puppy.
Good luck.
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