I just realized that IceWM supports both a startup script, and just as cool, a shutdown script.
When you select “Logout” from the IceWM menu, IceWM checks the /home/username/.icewm directory for a shutdown file.
After tinkering with /etc/sudoers to give my mother the proper sudo privileges I added this .icewm/shutdown script:
Now when my mother logs out of IceWM her laptop will automatically shutdown. That will simplify my tech-support life!
Also some good info here: https://bbs.archlinux.org/viewtopic.php?id=40604