Sql-server – Database ‘MyDb’ is being recovered. Waiting until recovery is finished

_{Community wiki answer originally left as an edit to the question by its author:}

The problem was that the database property AutoClose was set on.

The solution was to set AutoClose to false.

You can restore the database files to other locations using T-SQL commands to do the restore.

I did a test, something like:

CREATE DATABASE TestDB
ON (FILENAME='C:\test\TestDB.mdf', NAME='TestDB')
LOG ON (FILENAME='C:\test\TestDBLog.ldf', NAME='TestLog');
GO

BACKUP DATABASE TestDB TO DISK='C:\Test\TestDB.BAK';
GO

DROP DATABASE TestDB;
GO

RESTORE DATABASE TestDB FROM DISK='C:\Test\TestDB.BAK'
WITH MOVE 'TestDB' TO 'C:\SomeOtherFolder\TestDB.mdf'
    , MOVE 'TestLog' TO 'C:\SomeOtherFolder\TestLog.ldf'
    , RECOVERY; 

This creates a database in one folder, takes a backup of the database, drops the database, then restores it from backup into a new folder. You should be able to modify the RESTORE DATABASE command to suit your needs.