I don’t know of any way to do this per-database, but you can definitely allow MySQL users to access any database they have permission for from outside th DH network.
Inside the Mange MySQL section of the Panel, click on the user name of the account you want to give outside permission to. Find the ‘Allowable Hosts’ box and put either an IP address or DNS name for the computer or network you want to allow to connect.
[[edit: Blast! rlparker beats me by a matter of seconds.]]