p.1 #2 · Want to trigger 430EX without firing 580?
You can disable the flash from the 580EX (from the flash's menu). However, note that it still might appear as if the 580EX fires, but it's just a pre-flash (to trigger the 430EX) and so is not captured in the photo.
p.1 #6 · Want to trigger 430EX without firing 580?
I have a 580II, 580, 430. Lots of fun with stands and umbrellas. Check your owner's manual. You'll cycle through the 'master' menu and find an option for on/off with a picture of the flash showing lines from the flash head to represent a flash of light. rotate the dial and you can choose on/off.
'Off' will still fire the signal flash like mentioned above. It does not contribute to the actual exposure.
EDIT - you responded before I posted. If you had doubts, the 580 light would show up in the photo, so remember to watch the shadows in the future for the tell-tale shadows from a shoe mount flash.