Thanks Beth. I really appreciate your instructions, but they seem very complicated to me, so in case anyone else is having this issue, here's a much easier solution:
1. Computer 2 has the custom toolbar set up, and computer 1 is the one you want to migrate it to. Make sure you can access comp 2 from comp 1 across the network.
2. On comp 2, launch Word and close all documents. Go to Tools/Templates and Add-ins and click Organizer and the Toolbars tab. On the left you should see the name of your custom toolbar.
3. On the right click "Close" and this will give you "Choose a File" window. Navigate to the Normal.dotm file on comp 1 and Open.
4. Select the custom toolbar on the left and copy it to the right. That's it, you are done. Go to comp 1 and launch Word, and your toolbar will be there.