I'm not sure I follow this.
Is there any reason for any government NOT to go into exile?
You write, that "another faction" can choose to install a puppet. But not if the exile government exists. Or?
IRL In Norway, the government and the king escaped and formed a GiE - but Germany installed a puppet governement (run by Quisling). The same goes for France where Vichy in everything but name was a puppet.
It'd make more sense that a GiE exists for as long, as there is no apparant government in your own country. Let's take Poland. After having been run over by Germany, everything is as IRL. But then Germany decides to reestablist Poland with slightly altered borders. This would result in two polish governments - one puppet and one exiled. Years later the war ebbs out with Germany in control of Europe and UK/USA independent etc. But they still have a few poles sitting somewhere in Washington, dreaming of one time returning to their country - and Poland is up and running with a new (puppet) government. Eventually the Exile government would cease - as in IRL.
How does this work, if everything goes as IRL? SU runs over Poland and establishes a puppet. The polish GiE gave up eventually. How is this emulated in the game?
There is nothing to stop Germany from proposing a peace treaty to Poland once they have overrun everything. I things work as they did in Hoi2 then
10% occupied Poland is forced to accept anything but a direct surrender. So if germany does that, Poland (POLA) gets its land back minus whatever cores Germany has (1914 borders presumably). exile gov returns, re-assumes leadership of the country, done. There would never be two Polands.
Now the USSR on the other hand can push Germany out of Poland and assume control of the provinces belonging to the Polish government in exile. Stalin also could give the Poles back their land. (But not though peace, since they weren't really at war, if things are as I assume they will be.) However he does not want the democratic government to return, so he goes and releases the People's Republic of Poland (PRL tag?) as a puppet. Since the PRL Poland gets all the provinces of the original Poland (POL), the exile government for POL is dismantled and there is only one Poland left.
Note that Stalin already saw the exile government briefly in control of Warsaw province when a partisan unit rose up and defeated the German garrison in August 1944. He noticed that, since he was not at war with the Poles, he could have helped POL return to the country by pushing the Germans out and letting the Polish units march into the provinces controlled by SOV units. If things work as they did in HoI2, then POL automatically gets control back over its provinces once it moves into them. But Stalin decided that this was not so desirable, so he let the Germans crush Warsaw and wipe out the partisan units. So when Stalin restarts his offensive in winter, all of Poland is again under GER control and he can assume control of it all, allowing him to decide the postwar future of Poland himself.
OFC the whole thing could also be managed through events, without the need for a PRL tag... Stalin wins the war and owns Poland, then he goes and pushes the button to trigger the event "The war is over and we can decide what to do with Poland". An event could cause the USSR to "inherit" the government in exile and then release it again as a commie puppet (under the original tag POL, just with a different political party in power).
