Multiple Applications Connecting to Same SQL Server DB

I am migrating an application that used Access as a database to a SQL Server (using SQL Server Express) based application.  I have little experience with SQL Server, so I'm running into some obstacles in the migration process.  One of the obstacles is that I intend to use 2 different applications to read from/write to this database.  When deployed, these applications will be run from separate computers.  For the initial testing, I wanted to run the applications on the same computer as I did when using MS Access.  

However, while the first applications connects to the database just fine, the second application encounters an "attempt to attach an auto-named database" error.  The connection string is the same for both applications, so I assume the second application is lacking permission or there's some exclusivity involved, but I don't know how to overcome it.  The first application is not always running when the second application tries to open the database, so I would assume it's connection to the database is closed, but I could be wrong, of course.  

Thanks for any help you can offer.