Obviously (I think), JavaScript in the browser will not access to the serial interface. The best you can do is to make your script to communicate (via Ajax?) with the server (which provided the page), and make a server side program (eg. in PHP to communicate with the serial interface (I don't know if PHP can do that out of the box!) to transmit the orders / informations.
Probably not easy...

Eesh; I was thinking that if I export my sketch as javascript (Processing.js file) I could modify a few lines to shoot a series of short characters (1,2,3,etc) to the receiving Processing sketch. Does that sound like im on the right path?

You could also check out: http://www.spacebrew.cc/ & http://docs.spacebrew.cc/

(never tried it myself)

Looks very promising. I'll dabble around and do some reading. Any other suggestions greatly appreciated as well.