Ordinarily, I’d say remove the kid. Oh, I am gonna get so flamed for this post, but so what.
Like it or not, society has standards of conduct. Letting a child scream in a restaurant and completely ignoring it is both rude and inconsiderate. If he can’t handle himself in public, he shouldn’t be in public. That simple.
One quote from cartooniverse: “That kid,and his parents, have a right to THEIR pizza too.” Agreed. However, the rest of us have the right to peace and quiet. I just had a thought–don’t most restauraunts have “crying rooms” now? Just brainstorming. 
Former US President Ronald Reagan is in an institution right now. Why? Because he has Alzheimer’s and can no longer cope in our society. He’s lucky that way–as a former US President, he has enough clout to get the best care available in the US. But what about the rest of us?
A quote from Eutychus55: “Because my kid are as much a part of society as you are and I refuse to put them away for your convenience.” I don’t know about your kids, nor do I pretend to know, but some kids do need hospitialisation. Pour on the emotion all you like–that’s just the way it is. If you can’t handle the load–again, I’m not saying that you personally can’t hack it–get help from someone who can. Don’t you think that such children would be better off being cared for by trained professionals? IANAL, but if a special needs kid is REALLY messed up, a judge can order confinement (not sure about that, though). Whether you like it or not, you don’t have the right to allow your child to be disruptive. Accept it.
IMO, this is a case where emotion has come in so strong, it’s impossible for each side to really hear what the other is saying. Can we try to put aside the emotion and look at the facts? You can’t debate emotion, as that can go all over the map, but facts/logic don’t.
Full Disclosure: I was a total brat when I was a kid. I bet a lot of Dopers were, too.
I had/still have ADHD, but it seems to have subsided for the most part. Even to this day, following a simple list of instructions is a pain in the ass for me. My heart goes out to the parents of those kids–God knows I couldn’t hack it.