I think the book that might best suit your needs is Dickey's Empire of Mud: The Secret History of Washington, D.C. There are plenty of works that cover Civil War Washington, but Dickey's book examines the whole 19th century history of the city. Accompanying that, I'd suggest Scott Berg's Grand Avenues, which examines how L'Enfant came up with the plan for the city. It's a bit too early for the period you're talking about. Similarly, James Borchert's Alley Life in Washington is a bit too late — it starts in the 1850s but is an older but good look at the city between 1850 and 1950.