After re-reading your original post, it looks like you may be using the correct client (As you mention you have the mirror instance set)

As a troubleshooting test I would failover the server and see if you can create a connection to the mirror only - set it as the primary server, as if there were no mirroring.

What king of authenitcation are you using NT or SQL? SQL users have to have the same SID on the principal and the mirror (otherwise they will be a db orphan when flipped to the mirror)