Good job simplifying my convoluted explanation. Only correction is that people have to switch step 3 and step 2. It won't let you enter your account in turning on sharing on the wife's computer until you authorize your account on her computer.okay... hope this helps.
i assume you both use separate accounts for itunes?
1. I dont know if this needs to be done, but under preferences > sharing tab, select "share entire library"
2. turn on home sharing for both computers. use one username for both computers for home sharing.
3. authorize your account on her computer and authorize her account on yours. if you are using windows, it is under store > authorize computer
as others have said before, the drop down list only appears after the other person's library has fully loaded onto your itunes
good luck
So, authorize your account on her computer and THEN turn on sharing on her computer using your account name and password.