Ooh, I just now completed a similar project with 3 Calibre libraries! I used the
Copy to library function, which I did not even know existed till today. If you don't see the
Copy to library button on your toolbar, you can add it by going to Preferences, Customize the Toolbar. It'll be on the left (Available Actions); just add it to Current Actions. Then, just choose the book(s) you want to copy, click the copy button and choose the library you want to copy the books to and, voila, it's done. I've been wanting to do this for ages but couldn't figure out how till today.
In case I'm not too articulate, I hope someone else will be able to help you
(Btw, I'm using a PC so I don't know how it'll work for you)