You need to set your wow to windowed mode.

1) Press ESC to bring up the menu
2) Select video
3) Top right corner has a checkbox called "windowed" check it. wow will now be windowed.
4) Close wow down.
5) Restart your first wow client.
6) click the same link again and another wow client will open (Alt-tab between them) (if first wow started maximized but still windowed press your windows button)