I know it's a huge topic which is why I'm asking for book recs, though Reddit answers would also be great! The more specific thrust of my questions are somewhat described below:
I'm interested in how the day-to-day life of the emperors might have looked like - both that of hardworking, powerful emperors, and those who were more hedonistic/weak/shirked their duties. What did a court session actually look like? If the emperor had to be in mourning, what did he do all day? And how were their relations with their mothers, sons, daughters? Did they get together/eat together often, or were their lives pretty much separate? Did that lead them to be closer to the eunuchs attending them than their family members?
And what was the childhood of a prince/princess like? Given how often princes seemed to have just murdered their siblings, were they not raised together and thus had no familial attachment to each other? Were they just privately tutored and grew up confined in the imperial palace? Did they ever go out or interact with children their own age? Who raised them? Etc.
Thank you so much if you can help provide any sources/answers!
Volumes III and IV of Hans Bielenstein's The Restoration of the Han Dynasty accomplish exactly this, with a laser focus on the early years of the Eastern Han court following Emperor Guangwu's reunification of China. Volume III contains a detailed exploration of the imperial family while Volume IV does the same with the court. Both volumes are available online (for free). Despite their age, I have found both to be very accessibly written. Rafe de Crespigny's Fire over Luoyang also contains detailed descriptions of Eastern Han palace and court life.
Patricia Buckley Ebrey's Emperor Huizong is a recent, very detailed treatment of the Northern Song imperial court before its collapse. Lots of details on Emperor Huizong's palace life. He's an interesting figure in that he presided over an indisputable cultural zenith but also the military collapse of the northern Song.
Ray Huang's 1587: A Year of No Significance is a brilliant exploration of the Ming imperial court with extremely detailed depictions of the Wanli Emperor's daily life and court sessions (when he wasn't boycotting them, that is!).
Another personal favorite, although its focus is more on political affairs (very much including within the imperial clan) than the practicalities of daily life, is R.W.L. Guisso's Wu Tse-T'ien and the Politics of Legitimation in T'ang China, available for free online.