One of the reasons people get so overwrought in this kind of discussion is that there are people like this mother, who have no class and no consideration for others. If your child is not invited, don't bring him. If you've been asked not to bring your child, don't bring him.
An ex and I had a dinner party years ago and this couple thought it would be a good idea to bring their darlings. Mind you, this was kind of late - eating around 8-ish- and most of my time was spent putting milk in sippy cups, finding a bag to put a dirty diaper in, trying to get dinner on the table while avoiding the kids running around in the kitchen while the parents proudly bragged about school, play dates, etc.,... THEN, I had to make pb&js for the kids because they didn’t like what I made while everyone else was sitting down eating.
Grrrrr....... I still can’t stand that couple.