So, those of you "appetizers are always to share" posters, what about desserts? A couple of us have touched on it, but what do you think?
I stated in my post that IME appetizers are always shared unless they're order in lieu of an entree. Before I answer your question about the dessert, I'd like to clarify that statement in a couple of ways.
1) What I'm thinking of as an appetizer is sort of platter of individual pieces of whatever the appetizer is: cheese sticks, potato skins, asparagus spears wrapped in ham, etc. I don't recall ever seeing a restaurant appetizer with only 2-4 pieces, either. I'm thinking more along the lines of 8-12 pieces (a sampler-platter type appetizer might have 3-4 pieces of different items, but several items). To me, such appetizers appear to be sized and presented with sharing in mind. Apparently small appetizers sized for 1-2 are out there, but I was not aware of such a thing when I posted.
2) Like Judah, I make the "starter" vs "appetizer" distinction. I don't think of something like a soup or salad served before the entree as an "appetizer"--to me that means one of the platter-type things I described before.
3) While I think of appetizers as something to be shared, I would never presume that I was invited to share someone else's appetizer unless invited. I would never order an appetizer without planning to share (unless it was ordered as an entree), and I would be quite surprised if a member of my family or one of my friends did. However, I assume that the person who ordered the entree will offer it to whoever they wish to share with, whether that's the entire table or a subgroup. Or they wouldn't offer to share with anyone, and I would be surprised and file it away as a new data point in my experiences of appetizer-related behavior.

In the case of the OP, I would expect the mother to have the right to offer up a platter-type appetizer that
she purchased for sharing, even if the child chose which one to order. Now that it's been clarified that this was a small, individual serving-type appetizer, that sounds more like a "starter" that wouldn't be shared.
Do desserts have the same rules? Are you required to share them as well?
(And, to all posters, what do you do if you don't want to share, but the waiter brings forks for everyone making you feel like you have to anyway?)
I don't expect desserts to be shared, although it doesn't surprise me when people offer. The appetizers I have encountered in restaurant seem designed to offer several portions worth, both in size and in presentation as small, individual finger foods. The desserts OTOH usually seem designed as a single portion, at least in presentation (restaurant desserts often seem quite large). I'm thinking in terms of pie, cake, ice cream, a brownie, etc., which is the kind of thing I'm used to seeing in restaurants.
If the waiter brought extra forks? It's not something I've personally run into (I rarely have room for dessert in restaurants), but I hope I'd say something like "Oh, no thank you. I don't need any extra forks." And if anyone else at the table indicated that they expected to share my dessert: "Oh, I was planning to eat the whole thing. Do you want to order something now? I'll wait." And then, if they wanted a dessert and mine wouldn't suffer from sitting until theirs came out, then I'd wait to eat with them. Otherwise, I'd go ahead and eat mine and then sit and chat while they waited for and finished theirs.