After watching the video, I tend to agree with your behaviorist. This does not look like aggressive behavior, but indeed frustration. But it's very difficult to tell from a video.
Who feeds the dog? I would have the kids do it every meal. Make the dog look to them for his food and perhaps he will see them in a different light. You can have them stand one on side of the gate with his bowl and then they can set it down on the other side. If they can't reach over the gate, then figure out a way for them to feed him smaller portions through the gate. They can sit down while he eats. The idea is to associate them with something he desires and needs and finds pleasant. Have a parent supervise this exercise and watch that he doesn't try to nip them. They should also be participating in his training, so that he learns to respect their commands. But you need to make sure they are training him correctly, so you don't foul up your own work with him.