Try installing Nova Launcher and have them use that "always" (instead of the default TouchWiz launcher). Lock the desktop and the worst that will happen is a notice that the desktop is locked - the apps won't move. (And you can save the current configuration, in case they really mess up the locations of the icons.) It's easy enough if you want to move icons - just long-press the lock on that notice and the desktop unlocks for about a minute.
Welcome to Android Central! In the Settings>Accessibility menu, there should be an option for Touch & Hold Delay. You can set it to a longer interval, meaning the person has to press and hold an icon for longer before it can be moved.