This article is for Site Manager, please determine your account type with this guide.
See this article for customing AWStats to operate with separate secondary domain names. http://kb.westhost.com/questions/1254
1. How can I allow anonymous access to view the awstats report for one domain only?
There is a directive that can be modified in this instance. See http://awstats.sourceforge.net/docs/awstats_config.html#AllowAccessFromWebToAuthenticatedUsersOnly
2. By modifying my AWStats install in this way, will I lose the previous stats?
All materials will be preserved in the original install. New data will be gathered into the separate locations. It's also good to keep a backup of the prior months/years of data, backup the /var/lib/awstats folder.