My group dining expectations is this:
-If you order a group type appetizer (cheese sticks, calamari, fried mushrooms) that comes in pieces then you offer some to your dining companions.
-If you are dining with a group and only one person orders an appetizer but you and other's don't then when you are offered part of the app you decline. If the person who ordered the app stops eating it and it's just sitting there, it is fine to say "you know I think I will try one". You can also accept if the person who orders it says "No really, take some. I just really wanted some calamari but if I eat all of this I won't be able to eat my main course."
-If you are dining with just one person and you want an appetizer you discuss options with the your dining companion. Actually, I beleive in any group dining instance you should ask your companions if they plan to order an appetizer because if everyone says no, then you should ask if they are ok with you ordering one since your request will delay them getting their main course at most restaurants.
-If you order an appetizer that is obviously meant for one person such as a cup of soup, I see no need to offer to the other tablemates.
I've taught my kids the same rules so would be very suprised if they ordered cheese sticks and didn't offer some to others. My kids were also swimmers and I know how hungry an after practice teen or tween is, but that didn't give them the right to forget what I consider to be their etiquette rules. I would have done similar to the mom and picked up the cheese basket and offered to the other dining companions because I would have thought my DD's hunger had taken over her ability to be gracious.
On the dessert discussion I've also seen instances where one person orders a dessert while the rest of the table turns it down but still the waiter brings multiple forks or spoons. I always find this preseumtious of the waiter.