City of Djinns by William Dalrymple (1993) — Dalrymple spent a year in Delhi researching its layered history, and the book remains one of the best introductions to how Indian cities carry their past. Not specifically about Jaisalmer, but essential for understanding Rajput history and the culture of the desert kingdoms that produced the forts and havelis you are looking at.
The Maharajas by John Lord (1971) — A portrait of the Indian princely states and the rulers who ran them, written just after the Indian government abolished the privy purse. The Jaisalmer chapter covers the Bhati Rajputs and the peculiar isolation of the desert kingdom. Now out of print but findable in secondhand bookshops or libraries.
A Princess Remembers by Gayatri Devi (1976) — The memoirs of the Maharani of Jaipur, covering the end of the Rajput princely order from the inside. She grew up in a world very similar to the one the Jaisalmer nobles inhabited, and her account of how that world ended — partition, independence, the integration of the states — is vivid and elegantly written.
The Discovery of India by Jawaharlal Nehru (1946) — Nehru wrote this in Ahmednagar Fort prison during the independence movement. It is the best single account of how India understands its own history, and the sections on Rajasthan explain the culture of warrior kingdoms and desert trade routes that shaped cities like Jaisalmer.