I would desensitize the horse like Kevin says, only I do it while I'm hold the other end of the lead, that way the horse can move around, and get rid of his fear in a constructive manner, rather than pulling back on a lead rope, potentially causing harm that way. I just move in a circle with him, and keep the pressure on. Either way is acceptable, depending on how well the horse ties.
I would also work with a variety of different 'rope type objects', whips, longe lines, and softer more tickly things like polo wraps...never take the pressure off til he accepts it. I also would not use this horse for the kids until this issue is resolved. When he has been desensitized to those things on the ground, then get on him, and start doing that from the saddle, and again, don't use him with kids until you are sure he is okay with things touching him all over. A horse used in a program like yours HAS to be unflappable.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."