I have to say, that while there is always a risk of unruly children spoiling a meal, I have to say in the nearly 10 trips to disney I have done over the last 13 years, I have been pretty fortunate that that has not ever really happened. One thing I attempt to do to try to minimize the likelihood of it is aside from my first trip to Disney, I don't go during the summer which would have the most children, and also, I go to alot of signatures as well.
But maybe I have just been lucky, but I have also done many, many character meals and character buffets, and I have never had an experience where children ruined my experience. I am always worried about it because I hear other Dis-ers' horror stories, but aside from a bit of kids running around and obviously, some messiness at the character buffet stations, I can't say kids have ever ruined a meal for me.
I also don't really do food court or outside quick-eatery fast food style meals much, I mostly do the sit-down eateries and I eat at alot of resort's restaurants where I find better behavior as well, and less kids.
Another restaurant you are almost assured of not encountering any kids at all is Monsieur Paul, the upscale French eatery in Epcot. Generally, while kids pop up everywhere LOL, of course, you do see less of them at the more upscale signatures in the resorts. Narcoosees is another one of those out of the way signatures where you are likely to have a quiet and near kid-free dining experience. Some of the more expensive Disney Springs ones as well - I had a very quiet and kid free experience in the Wolfgang Puck Dining Room restaurant. (it's closed for good now, though)