Opening just a new frame isn't enough for you? I don't know about Aquamacs, but in Emacs It is in the file menu or you can use the command Ctrl-X 5 2 .
Yea, but why wouldn't it let you run two instances? I'm not an Apple user, so I can't give any advice, but it strikes me as an odd limitation for a text editor.
That's a generic OS X (mis?)feature. The OS tries to detect when an app is already open, and forward you to the existing instance rather than starting a new one. You can see this behavior spreading into other apps like firefox which try to prevent multiple instances even on other platforms.
Anyway, try "open -n /Applications/Aquamacs\ Emacs.app" on the command line (e.g. in Terminal.app). I'm not sure whether a gui equivalent exists.