I'd like to first say your feelings are appropriate and justified. Clearly the kid was wrong, and mom even moreso for not quickly addressing the situation. The ball was in her court. She should have reprimanded the kid and told him his behavior was rude, and then made the child apologize and clean up the mess, and then lastly should have followed up by giving you an apology. Unfortunately, it seems more and more people think allowing children to be selfish and rude is somehow building up their character and initiative. Big mistake..and clearly a reflection of how this woman probably operates in her own daily life.
With that said, I hesitate to agree with everyone on the appropriateness of directly addressing a stranger's child. Whether the mom and kid were right or wrong, I think confrontation of a child is a breach of boundaries. It borders on being equally as rude, and in some cases might even set a bad example for your own children. (Bullying back or sinking to the level of the accoster by lashing out verbally at people in retailiation of rude behavior.) Clearly mom didn't see the child's behavior as disruptive and rude. I think mom's the one who needs to be corrected. The child is only doing what he's been taught by mom.
I guess if it were my kid who was acting up, I would be pretty freaked out if a stranger reprimanded my child. I wouldn't know if the person was a wack-o, or how far the confrontation would go. It certainly would put me as the child's parent and primary protector on the offensive, and depending on the situation, who knows where things would go next. I guess I would say maybe it's better to put the emotions in check, and instead of reaching to the childish level of both this mom and kid, I would have taken on a parental role and shamed them by doing one of the following instead:
1. Flag down the waitress or manager of the restaurant and explain loud enough for mom to hear that the child across the way is throwing food at patrons, and insist that you would like them to talk with the woman about it and even suggest to ask the manager or waitress to ask "her" to move to a different location. In this case, the manager will be forced to either ask her to just go, or will force her to apologize and act as a sort of mediator to resolve the problem, and if she looks like a "nutty-one" leave shortly after so she can't follow you home in your car and cause more trouble! These days you just don't know. LOL.
2. You could announce to your children loud enough for the woman to hear across the way "Don't ever do what that boy is doing. He has terrible table manners, and is being rude to everyone in the restaurant. His mom should buy you another lunch or make her boy clean up and and apologize." Then flag down a waitress and ask her to move your family or hers because the child is throwing food and be sure to explain the mom isn't doing anything to stop it. Bad-mom'll either ignore you, or feel real embarrassed because hopefully everyone else is seeing the hullabaloo..and just leave herself.
3. You could directly address mom and say, "I don't appreciate your child throwing food. Could you please ask him to clean it up and apologize to everyone in the room for being rude?" She probably won't like it, and may even get nasty. But remember, if you can keep your cool, SHE'LL be the one the restaurant manager asks to leave the restaurant if SHE gets aggressive or rude.
I'm sorry this happened. I totally think she's wrong and your're right in your feelings. I guess I'm saying don't let her bad behavior become a negative teaching moment for your children, and yet another opportunity to reward bad mom's bad behavior. Stick to your guns and be victorious all around. I hate to see the bullies get their way. Even when they're grown!