Small update to the My Maps support in GoKML, announced a few days ago; you can now edit the links contained in the file. Just goto your secret admin page, generated for your link.
People viewing your file in Google Maps will see the update soon, Google Maps caches it for a while.
People viewing in Google Earth however will not, as they downloaded a static file, which brings onto another point, if want them to auto update as well, could create a network link to your Container, using the standard GoKML form, (enter the url your container and choose appriate refresh period).