In situations like this, it's tough to know what to do. Obviously, the first best way to take action has already been discussed -- it needs to be handled by the parents, using some common sense. A young child probably doesn't need to be up that late. If they are, it's likely they'll be fussy. Not taking this into account points to how inconsiderate those parents are of others. It's something the conscientious would think about.
Failing the parents' good judgment, the restaurant -- particularly one that's upscale, needs to make it a priority to ensure the comfort of all their guests. If one guest is causing the discomfort of countless others, well, it goes without saying the restaurant has the right (arguably even the obligation) to do something about it. Even a young child is a customer and should be treated accordingly. After all, wouldn't they throw a loud, obnoxious drunk out if necessary? Of course.
Obviously, this is a sticky situation because it requires a judgment call on the scene at the moment. If things are really that bad, and the staff knows it and patrons are complaining about it, the restaurant should do something. Not to is, well, just rather foolish. Why not have a few unhappy customers instead of a room full of them?