How can the same database from one site be used on another website?

Using Visual Studio 2005 with SQL Server Express 2005 on MS Server 2003 with II6.

I have two sites on the same server (the same drive).  I would like to use the database from on site for another site.  Unfortunately, when the (site B without DB) access the other (site A with DB), it creates a duplicate (ASPNETDB2005.MDF) in App_Data directory on the (site A without DB).  I would like to only have on database to keep both sites in sync.  How do I configure (site B without DB) to just use the  (site A with DB) without making a copy.

Below are some highly modified (web.config) settings:
<connectionStrings> <add name="Identical_other_site" connectionString="Data Source=.\SQLEXPRESS;AttachDbFilename=C:\SiteWithDB\App_Data\ASPNETDB2005.MDF;Integrated Security=True;User Instance=True" providerName="System.Data.SqlClient" /> </connectionStrings> <sys ...