How to prevent Finder from waking up the second hdd?
The files are being accessed in read-only mode - the r in the fourth column, the file descriptor column, indicates this. 

Is this a media and/or backup drive of some sort? 

In any case, I believe Finder is opening those directories because the volume is mounted. Even seemingly innocuous actions may call Finder to wake and read the drive, such as opening a file browsing dialogue in another application.

You may try removing from the Sidebar of Finder any folders on that drive. Also go into Finder's preferences, go to the 'Sidebar' tab, and uncheck either 'Hard Disks' or 'External Disks' under Devices, depending on whatever drive this is. That might prevent Finder from calling the drive.



Barring that, you may try try checking off Put hard disk(s) to sleep when possible in the Energy Saver's preference pane, which will keep the drive awake perpetually, and avoid pauses while it wakes.

 

You may also want to run ps -ef to check and see if there are any background processes that may be indexing or calling the drive.