Hi,
Thank you for your post.
According to your description, I’d like to confirm whether you want to work in the two sub sites that the homepage (root) has anonymous access and another sub site are still asking for authentication.
Based on my experience, you may create three publishing rules in the same order as mentioned below:
Rule 1: SharePoint publishing rule -> Publish specific Directory in the paths (Default is Root) -> Use the web listener -> Enable "Single Sign on" on the web listener -> Use Authentication
Rule 2: SharePoint publishing Rule -> Publish the Sub site for anonymous access -> use the same web listener used in the rule 1 -> Under the rule properties, under Users tab, remove "All Authenticated Users" and Add "All Users"
Rule 3: SharePoint publishing Rule -> Publish the Root directory using "/*" -> use the same web listener used in the rule 1 -> Under the rule properties, under Users tab, remove "All Authenticated Users" and Add "All Users"
"All users" option in the rule properties bypasses the authentication required on the web listener
Meanwhile, I have list the following articles related to MOSS Authentication.
http://meiyinglim.blogspot.com/2006/07/part-2-enabling-anonymous-access.html
http://www.andrewconnell.com/blog/articles/HowToConfigPublishingSiteWithDualAuthProvidersAndAnonAccess.aspx
Hope this helps.
Nick Gu - MSFT