You can go ask this at Apple Support and compare the further advice you'll get with what I'm about to tell you : http://discussions.apple.com/category.jspa?categoryID=149
Here's what I would do.
The new iTunes 7 series allows you to re-import music from the iPod : http://docs.info.apple.com/article.html?artnum=300173
Copy down the user ID/password, etc, for the account if you haven't done that already.
So, on the new computer, download and install iTunes, recreate the account and just follow the instructions for copying the files.
Authorize that computer and play all the music so that you know all is working well.
Now, that iPod can be switched to manual and used as a usb drive.
Once you're sure the music's safe use it to transfer music in iTunes from the other computers.
From your description you will be using two computers for iTunes, one for your wife and daughter and yours, so deauthorize any other computer with iTunes on it and uninstall iTunes.
iTunes lets you authorize 5 computers and an unlimited number of iPods.
Great, all the music in one place now.
Put the songs you want on your "inherited" iPod on a play list and burn them to disk for transferring to your computer.
You now have all the music in one place and can add those songs back to iTunes.
On your computer you are not importing, you are transferring files.
The reason you're getting that insert CD notice is because your clicking the wrong function from the drop down menu.
You want Add Folder...
That will send to the window with all the folders listed pick the one with your mp3s in it.
Treat the files you burned to cd in the same way.
When your daughter gets her new iPod and you get the old one, format it and set up your play lists for your own music.
You can legally use hers as well as your own.
What you can't do is sync your iPod to her computer or hers to yours.