Seems like there was one in France, that moved to the UK, there was another in Iran? And maybe a third one? I'm not sure. Two is already a lot of governments in exile.
Edit: with further reading, it seems that there was only one government in exile, but I still have a few questions regarding how and why they coordinated with the Soviets (after Katyn especially).
It looks like you sorted out part of your question, but as to your edit, cooperation was a touchy issue, and the revelations of Katyn actually resulted in a breakdown of relations between the two governments. I touch on this more in this older answer, which also touches on the other aspect of your question regarding Iran.