Two excellent Arabic sources on the crusades (and on Saladin) are both translated into English by D.S. Richards: The Rare and Excellent History of Saladin by Bahāʾ al-Dīn b. Shaddād, and The Chronicle of Ibn al-Athir for the Crusading Period. /u/parsonsperson's suggestion of Usāma b. Munqidh is also a good Arabic source on the period more generally (translated by Paul Cobb).

In addition, there is another volume contributed to by Cobb and others entitled Saladin: The Sultan and His Times, 1138-1193, and, probably more interestingly for you, a new book has just been released entitled simply Saladin by Anne-Marie Eddé, and may be right up your alley.

There's room for more recommendations, but the AskHistorians Book List (see link in the sidebar) mentions The Crusades: The Authoritative History of the War for the Holy Land by Thomas Asbridge as a good book and says it is heavily focused on Saladin and Richard in the Third Crusade.

I think that Kitab al-I'tibar (trans. The Book of Contemplation) by Usama ibn Munqidh is a great read. The author was a member of Saladin's court. He devotes a sizable chunk of the text to discussing Frankish customs during the crusades as well as more general topics of life in the Levant.