Depending on your database implementation, often you will be able to link tables from another database (the AdminDB) and have them appear in your various module databases.
In Microsoft Access you can link tables by right clicking, and then choosing an ODBC data source. In Oracle they call it a database link. I'm willing to bet SQLServer has some form of this implementation short of implementing custom replication on a single table.
Once you link in your foreign admin tables to your module databases (or vice versa), then you should be able to define constraints as if the tables were within the same schema.
A second option may be even simpler. What if you used the same schema for all modules and admin database? You know the admin database is present, so simply run the table creation script against that schema. As long as there is no table / view / stored procedure naming conflicts, then it should all work just by changing the dblogin in all modules to match.