403's usually result when index browsing is disabled and/or permissions deny reading the content directly.
But if it works in one browser and not the next, it's likely one of these two scenarios: First, authentication is required but the webmaster of the site issues a 403 instead of 401 (not authorized) to fool people. Second, it's setup properly but the webmaster no longer hosts the site and don't provide a redirection to a new URL. In this case it is not unusual for the 403 error to be returned instead of a more helpful error, and the problem usually goes away in a week or two (DNS propagation globally) if true.
Your child's Mac might be caching old page data, or successfylly authenticated prior to the site being moved, and on your computer you see the 403 as anyone else would who isn't logged in or visiting the first time.
-jim