Hi Susan
I just did a bit more exploring and found Capt. Adlai Hardin's pension records. It is very interesting because it shows 2 spelling os Adlai's name, and also shows that Cordelia went by her nickname, Dixie. Also it has his death date. I thought you and anyone else looking for information about Adlai and Dixie might find this interesting!

Taken from CARAT, Catalogue of Arkansas Resources and Archival Treasures
Arkansas Confederate Pensions
Surname: Hardin
Given Name: Adlai (Adley)
Application Number: 24469
Widow Surname: Hardin
Widow Given Name: Dixie Ophelia
Company: B
Regiment: 2
State Served From: North Carolina
Division: Cavalry
Pension County: Lee
Death Date: 12/26/1925
Application Year: 1916
Widow Death Date:
Comments: widow applied 1926 / questionnaire