Hi John,
When a report is scheduled, it's running using the service account assigned to Crystal Server. If you are getting prompted twice, that usually means the report can't find the database to connect to.
If you can go onto the server Crystal Server is running on, go into the ODBC administrator and see if you can create an ODBC connection to your local database and test the connection.
You are correct that if it works on one database and the second database is configured the same, the report should work. Because the report is running on the Application server and not your local machine, I'm curious to see if the problem is a simple issue of the two machines not being able to communicate with each other.
Not to overlook the obvious but make sure the SQL Server account you are using in your database configuration is active in your local database as well.
Is your local database set to use SQL Server Authentication or Windows Authentication? It should be SQL Server Authentication to make sure the account you are passing is being used and not the Crystal service account.
Good luck,
Brian