It could just be however much the countries like each other? Or however much one of them is a pushover and can't kick the other out/escape. And maybe how much they rely on the sovereign nation, but that still doesn't quite make sense because you know that if they could have America and England would have been living together. We didn't see France with Germany, even after his surrender in canon, so he doesn't seem to have been the same as Austria at least. He probably had the same deal Denmark has? Or maybe everyone was just smart enough to know this was not going to be a happy household, with France, Austria, Prussia and Hungary all under the same roof.

Case by case basis? How self sufficient a nation is? I'm not sure if China and Hong Kong live together either, HK is pretty self sufficient in everything except military but he's technically Chinese soil so I don't know.