Is there anyway to test if a module already exists on a page and then have it not be allowed to add to the page

OR

remove it on first load if its the second instance of a module?

I'm assuming you're talking about one specific module you're coding and not any modules in general.

I'm blueskying here but how about this? On module INIT it checks to see if the logged in user has admin credentials. If "Yes" then you remove the instance of the module from the dropdownlist in the control panel.

That's the only thing I can think of off the top of my head that wouldn't require a core change.