How does Time Machine handle an external drive shared between two Macs?
Time Machine allows you to backup multiple macs to one drive.  You just plug it in, set it up, and you're good.  If you look at the file system, you can see separate backups for both computers.  At our home we currently do this with a Mac Mini and a MacBook.  The Mac Mini is always plugged in, and the MacBook gets updated every couple weeks.  We use a 1.5 TB drive from Western Digital.  Given your description, I think this solution with your 2TB drive should work well for you.

The data backed up by both macs will not be the same, as no matter how hard you try, both computers will wind up having subtile differences, so the data won't be "exactly" the same.  Backing up only one system doesn't seem ideal to me, but you can restore a MacBook from a Mac Mini backup.  It works fine.

Also, you realize that the drive must be connected for you to access the photos and music that you have stored there.  You'll have to factor that into your storage solution.