If each of your browser clients is connected to your server (you say
you are writing it in Twisted?), then all you need to do is make your
server pass the message along to the other client. To do this, you
probably want to keep a dictionary of connected clients somewhere
keyed by some identifier (perhaps username or similar), and develop a
protocol for addressing a specific one in the upstream messages. I
think Michael or Mario put up an example Twisted-based server which
sends framed messages between clients. Maybe someone will chime in
with a link to some code you could look at.
Hope that helps,
Jacob