So he is fine being led and then throws fits and starts to bolt after the lead rope is off? This was a similar thing to my pony, back when I wasn't in control of him, or higher on the 'totem pole', but my Dad was.
From what I think, when you are leading him around, he is content to do as you ask. If your kids are not higher on the totem pole, in his mind, he can do what he likes, therefore he begins to buck and bolt. If your kids step above him due to groundwork, he most likely will settle down and behave.
Since your kids have ridden him again, and have come off, it has unconsiously reinforced his bad behaviour. He knows
he can throw people off, so he has won every ride so far. He will continue to do so untill someone small enough can get on him, hold on and teach him that his behaviour will not be put up with.
It also sounds like he needs lots of ground work so he will stand nicely, ground tie and wait patiently for anything that you ask of him. Working with a trainer would benifit all of your family greatly.
Like Spastic_Dove stated, I would not continue to put your children on him untill you can find a way to have him trained. :)
Best of Luck and I hope that things work out for you quickly!