I must say I'm stunned to hear that some people think appetizers are always shared by everyone at the table. And I must be eating at all the wrong restaurants because all of the appetizers I've ever ordered would never be enough to pass around a table full of people - three medium stuffed mushrooms, two silver-dollar-sized crab cakes, eight tiny mussels or baby clams, five shrimp, or three half slices of melon wrapped with prosciutto. It's generally only a few bites meant to whet one's appetite for the meal to come. Something like a hot or cold antipasto or pu pu platter, which is many times more expensive than any other appetizer, would be an exception to this.
When we eat out with family, we often share two or three appetizers, but that's generally because we're paying the bill and our guests are too polite to order individual appetizers. When eating out with friends, someone will generally ask if we want to order a few appetizers for the table or else someone will announce that's she's ordering the X and ask if anyone else would like to share it. But we often order our own appetizers without sharing.
DH and I have been married 46 years. We ALWAYS cut a small piece of our entree and place it on the other's plate to sample. If either of us is engrossed in conversation and forgets to do this, neither of us would just reach over and take a small bite, even though the other would never mind. DH doesn't care for olives, and if some sneak their way into his food, he passes them to me. I would never just help myself to them without asking. It's even more important to extend the basic courtesies to those closest to you than to friends or acquaintances. To me, this is especially true with children, for whom we are supposed to be modeling appropriate behavior. So I feel that the mother was very rude indeed.
In my mind, assuming that an appetizer is always shared by everyone at the table may be a custom in some circles or areas but it is not required by the dictates of etiquette.