Pygame with Multiple Windows

The short answer is no, creating two pygame windows in the same process is not possible (as of April 2015). If you want to run two windows with one process, you should look into pyglet or cocos2d.

An alternative, if you must use pygame, is to use inter-process communication. You can have two processes, each with a window. They will relay messages to each other using sockets. If you want to go this route, check out the socket tutorial here.