I had weird issues when I tried dual-boxing from the same install, but not the exact same thing you're having. But I'd still recommend copying your WoW directory to a second location, preferably on a different disk, and create a shortcut to the launcher.exe for that location on your desktop. I've been three boxing and have three different WoW directories. Just copy the entire World of Warcraft folder and you're good to go. I named my shortcuts WoW2 and WoW3 and have account names stored for each instance.

edit: As a side note, I've never suffered follower disconnect with multiple program locations. I even keep a copy in a USB drive to play at work or anywhere I can't install it.