There in lies the problem, as I understand it, you only get one profile, so the one not calibrated could be kind of funky. It seems like there should be some type of software out there to manage profiles.
I would have to check to make sure but I believe my Datacolor software allows me to calibrate multiple monitors and store the profiles for each. Then I can call up which one I want. But I only have one monitor so I can't test that part of it.
But it sounds like you want to calibrate both monitors and have the profiles applied respectively so both monitors can be used simultaneously. Maybe time for a new graphics card?
Same as RVT1K, my Datacolor software just works and I can't find much about it on the interweb.
I've got 2 monitors at home which are calibrated for my desktop, then I use the same monitors with my works laptop that's got the two monitors and its own screen calibrated all with seperate profiles. I've got an old Nvidia gtx950 in my desktop, and the laptop is running a low end ATI card (I think)