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.