Ok I could be wrong but the dream world seems to be a manifestation of yellow dragon's desires to live in the modern world with Dojin? He once watched Dojin forget him and marry a woman in his own world through a magical mirror so I'm guessing that's how he knows how the modern world works.
The true reality is the one where Dojin is an emperor. That doesn't mean Dojin's family are fake-- it's just he never went back to his original home. I'm guessing yellow dragon sent him to the dream world to keep him from harm? Because both times he's sent back are when his life was in danger and yellow dragon needs a moment to recuperate from a wound. The dream world can be breached though since the cat girl managed to get in.
I thought it was a dream that yellow dragon put him in and made the setting his life in the real world for familiarity I’m guessing...? And yellow dragon put himself in there too just to be beside him
Wait ? All of that ? Just a dream
I'm lost and confused