I finally got the sharing of our Address Books working. I was assuming that once you accessed a shared address book, you could drag a card from the shared address book, into one of the local groups. Then when it is updated remotely, the updates would automatically appear.
This is not the case. When you drag a card from a remote address book, it makes a copy of it locally. This means that updates don't happen automatically.
The next thing that I tried was to crate a "Shared" group in both address books. I copied all of the cards from the remote "Shared" group in to the local "Shared" group. This caused a bunch of duplicates. I tried using the "Look for Duplicate Entries...", but this didn't find any of the duplicates. I then manually merged each of the duplicate cards. Once I finished that, I did the same thing going the other way.
I want to write an AppleScript that would do this automatically, but it looks like Apple didn't put full AppleScript support for the Shared Address Books. When I run the following script, I only see the local groups, and not the groups from the subscribed address books.
It seems like if I really want to do this, there would need to be support in AppleScript.