Library folder access on remote drive

I can figure out how to access my Library folder on my drive thorugh all of the terminal commands and shortcuts on my start-up drive, but how about on a remote. I needed to take my MBP in for a new screen. It will be gone for a week. I cloned the hard drive to a portable drive, so I had access to all the data. I ran the Terminal command to make the Library folder visible, but during the 10.7.2 update, it hid it again. And I cloned it before checking. I went to import my Mail folder to a spare computer and I can't get into the Library folder on the cloned remote drive.

I figured I could find search for some files in Spotlight that would be located behind this door and that didn't work entirely. I need to get into Application Support and Mail folders. What would be the path directory to these on a mounted USB drive?