The dress code for the dining room at dinner is no shorts, and that is for children also.
I made all mine wear long pants last year. It also helps them start to learn there are certain codes of dress (and conduct) in different places, and they are required to go along, if they want to be included.
Just like here locally, we take them out to eat. If we are going to the local Mexican joint, shorts are fine. But if we are planning a fine dining experience on the Plaza, we will require them to dress accordingly.