Crittenden's father was US Attorny general under 3 Us Presidents. Replaced Henry Clay in the US Senate. His mother Sarah Lee 2nd or 3rd cousin of RE Lee. His brother George Bibb Crittenden was Brigade commander CS. Soundly defeated at Mill Springs Ky accused of drunkeness but "un-proven". My memory fails me at the moment but he was again accused of drunkeness at Shiloh or Corinth this time it was "proved". He served the remainder of the war "without rank".
I have found no letters diaries or books by any of the Crittendens you might try the Library of Congress.