I dont really understand that video, my PC doesn't look like that.
As long as you have itunes on both computers, all you need to do is authenticate her PC for your itunes account. Every itunes account can be active on 5 devices simultaneously. She wouldn't have your password, just the ability to play your stuff. (I havent dont it lately since my fiance and I share an itunes account, but this may enable cloud download now - making the below part unneeded)
If you open up the ipod in windows and really dig, you will find the songs in a folder in it. You can copy them manually. I cant remember the exact location. Will look now.
Edit: Google has a million articles on this, here is one. http://lifehacker.com/105256/how-to-copy-songs-from-your-ipod-to-your-pc