Disable repeated "You don't have permission to use the application" dialog boxes
You can disable the startup items entirely, so they don't attempt to run at login.
System Preferences → Users & Groups → (Kid's account) → Login Items
Select the applications that are denied, then click the minus sign to remove them from the boot process.
See also: http://www.maclife.com/article/howtos/how_remove_startup_items_os_x