That is not possible. If its one IIS WebSite its using 1 db because there is only 1 connection string so they cannot be using 2 dbs. At least its not possible for them to both be root level Web Sites like beta.somedomain.com and www.somedomain.com and use 2 dbs. You can run 2 sites like that from a single db using host names, or else you need 2 IIS Sites so they can have different connection strings.
Please be more specific about what you mean by this:
I then install another copy of the site on www.xxxxxxx.com
what exactly did you do.
Hope it helps,