After the battle of Prairie Grove, there are references to a 2nd Corps [no commander named] such as in the table of organization for December 12, 1862.

Vol 22 Part 1, pp 903-04
[excerpts]

Organization of the Army of the Trans-Mississippi Department, Lient. Gen. Theophilus IL Holmes, C. S. Army, commanding, December 12, 1862.
FIRST CORPS. Maj. Gen. THOMAS C. HINDMAN.

SECOND CORPS.
FIRST DIVISION Brig. Gen. HENRY E. McCULLOCH.
[3 Texas brigades]

SECOND DIVISION. Brig. Gen. T. J. CHURCHILL.
[3 brigades-Arkansas Post command]

Fourth Brigade. Brig. Gen. J. M. HAWES.
12th Texas Cavalry, Col. W. H. Parsons. 19th Texas Cavalry, Col. N. M. Burford. 21st Texas Cavalry, Col. Geo. W. Carter. Chrisman’s (Arkansas) battalion.

Fifth Brigade. Col. M. J. WHITE.
3d Missouri Cavalry, Col. Colton Greene. 4th Missouri Cavalry, Col. J. Q. Burbridge