Shogun becoming the emperor doesn't even make sense. What happens to imperial house of Yamato?
There were three shogunates, but yet they didn't get rid of emperors, because emperors of house Yamato have always been big part of Japanese society (even when they were powerless), disbanding that would have caused chaos and end of them who attempt it.
I'm not professional in Japanese history, but that is what I figured with brief reading.
Yep. I'm not an expert either, but as far as I can make out, the division of Japan we see at the start of the game represents the Warring States period, in which emperor was mostly powerless, and the Ashikaga shoguns were sort of in charge but had little power over the daimyo. It ended with a series of daimyo who managed to consolidate power in one person, but who had no official country-wide title, not even 'shogun', until Tokugawa Ieyasu was appointed shogun in 1603. The form of government ended up the same as it was before, at least on paper, except now the daimyo were too weak to rise up against the shogun and each other.
I don't really like how the special 'Shogunate' government has extra diplomatic relations - it's a fudge, and it encourages unified Japan to behave like the Habsborg, with diplomatic relations all over the place, which is the exact opposite of the insular attitude that Japan took in real life. Instead, I would make it so that Japan has *reduced* diplomatic relations; Daimyo vassals don't take up a diplo slot, but can fight you and other daimyo, and can't be diplo-annexed (instead, as shogun, you always have a CB to forcefully integrate them). Non-Daimyo vassals shouldn't be able to fight each other. That way, you can keep the same government for both the Ashikaga and Tokugawa shogunates.