I would like the children to have the ability to see a read-only view of all the settings and activity that the parents can see (via the web interface) --- either via the same web interface or perhaps on the monitored device they're using. But primarily the web history should be visible to the child. The reason I think this is important is to make a child realize they're accountable - so they can see what the parents know about their online activity.
That would be terrific!