I am just waiting for the time when something serious DOES happen. If one of their children ends up in the crossfire, the Phelp's should end up losing all their kids for negligence IMO. What do you think of a family exposing their children to a potentially volatile situation?
While they have taken to the airwaves as of late, unless an unbalanced person shows up with a gun, your imagined scenario is very unlikely. In past protests, the police are usually in evidence, and counter-protesters are kept apart.
People bring children to all sorts of contentious and volatile protest rallies. I can't recall any instances where children were physically harmed, and while IANAL, I'm not sure the parents would be held liable.