Windows IIS Authentication not working with FQDN but is without it
Is the FQDN in IE's "Intranet" security zone? If not you will need to add it in, or add in the *.mydomain.com wildcard.
The "Intranet" zone is inferred if you use just the server name (i.e. there are no dots in your URL), but often the "Internet" zone is used if you use the FQDN.
Windows Integrated Authentication is not automatically used for sites in the "Internet" zone.
http://support.microsoft.com/kb/303650