TortoiseSVN hangs when using a post-commit hook

The hook script has to finish first to make the commit succeed. So the client has to wait for that. If your hook script takes too long or doesn't finish at all, then the commit appears to hang.You can try to start the long-running command in your hook script in a separate process so that the hook script itself finishes immediately.

However: if OtherComputer is the computer you're trying to commit from and the script tries to update the very same working copy, then that won't help either: the update has to wait until the commit is finished, but the commit waits for the hook script running the update to finish - you've got a deadlock.

This looks like a local hook. I don't think you can use PsExec like that. I think you're opening the PsExec session on the other computer, and it just sits there. It doesn't have a way to see the next line in the script. i.e. the TortoiseProc isn't fed into the PsExec.
I think you need to install the SVN client (command-line client) on the other machine. Then make a bat file (updateme.bat), place it on that machine, then you can do something like this (all one line):

c:\sysinternals\PsExec \\OtherComputer c:\updateme.bat