If I can make a couple of slight tweaks to your work with Onyx - I learned the hard way years ago that giving fearful dogs treats can go very wrong as they will come closer than they are happy to get the treat and it can lead to a nip as they panic. I still bear the scar and try hard to warn people that treats should only come from trusted humans or if you feel the dog has progressed far enough get the new people to drop them on the floor.
With the kids if he is barking a few times he is a little too close, you would be far better to find a vantage point where you can watch and let him have lots of treats but not feel worried enough to bark. Once comfortable you can start to move a little closer day by day, but barking says you are currently too close.