You really can't automatically sync with 2 computers with different libraries.
You can automatically sync with 1 computer, and manually sync with the second, but when you sync with the first all the content from the second will be removed.
IF you had a duplicate copy of your library on 2 computers the iPod should be able to sync to both libraries, but there is not really a point to that because the content is the same on both. You would need to copy the iTunes Library from the home PC and put it onto the Work PC (delete the old library that was there). Anytime you add content to the home PC, you would need to add the same content to the work PC manually. This would allow you to sync to both.
Unless you want a duplicate library at work, you'll need to make your iPod manually sync with the work PC and drag and drop content onto the iPod from the work PC, knowing it will be erased when you sync at home.