How do I remotely destroy parts of my Macbook hard drive?

Check out TrueCrypt, specifically the section on "plausible deniability" and "Hidden volumes" where a steganographically hidden, encrypted volume is hidden withing another encrypted volume... sounds similar to the situation you are describing

If the lid is closed and you didn't configure it otherwise the machine is asleep and can not be remotely connected to. If you configured Wake-on-LAN AND you are on the same network you can wake the machine via a "magic packet" even when the lid is closed.

Remote access also needs to be set up ahead of time, so if they already have the device and you haven't set up Remote Login or something similar you are out of luck.

However, if you have SSH access you can delete the files from the command line and then shred the free space on the drive to prevent recovery. SSH access is (more or less) invisible to the person looking at the machine. Search for "secure delete command line mac" for details on performing the data wipe.

If you only have remote desktop access then you can perform the same operations but they will be visible to anyone looking at the screen.