As I remarked in a previous post, I don't believe there was such a formal organization as a 2nd Corps. Instead of a formal 2nd Corps, It would appear to be simply a defacto arrangement of troops not included in the 1st Corps:

SPECIAL ORDERS,
HDQRS. TRANS-MISSISSIPPI DEPARTMENT, Numbers 39.
Little Rock, Ark., September 28, 1862.
11th. The following arrangement of troops not included in the First Army Corps, Army of the West, is announced, viz:....................

Back in June, as Trans Mississippi District commander, Hindman's initial and primary military organization was styled the Army of the South West. As you well know, this force was hastily created to respond to the immediate threat to Little Rock.

After Holmes assumed Departmental command, Hindman was given various assignments including:

August 12, 1862. General Orders, HQ.Trans Miss Dept, # 2. Little Rock, Ark..
III. All the troops in the neighborhood of Little Rock and on the Ark River below will be immediately encamped on the Bayou Metoe, or at such other place nearer the enemy as Gen Hindman may designate. Gen Hiudman will assume the immediate command of the army thus ordered, and prepare it at the earliest moment possible for active field operations. By command of Major General Holmes

SPECIAL ORDERS,
HDQRS. TRANS-MISSISSIPPI DEPARTMENT, Numbers 39.
Little Rock, Ark., September 28, 1862.
9th. Maj. Gen. T. C. Hindman is relieved from the command of the District of Arkansas, and will assume command of the troops in Northwestern Arkansas, Southwestern Missouri, and the Indian Territory, and will organize the same into an army corps, to be styled First Army Corps, Army of the West.

On October 20, Hindman assumed command of the troops named in Special Orders #39. On October 25, he told Holmes that he ...will attend to organization of corps as soon as possible... has not had time to do so as of yet, though daily working on the details....

In special order # 38 of November 9, Hindman announced the organization of the 1st Corps, Trans Mississippi Army.

For years, I have assumed that an official 2nd Corps existed, if for no other reason than by inference. But, even with the detailed information found in the Alexander Papers, I have been unable to confirm the existence of a formal 2nd Corps.

Furthurmore, Hindman and Holmes were seriously discussing sending a Texas division [probably of 2 brigades] to reinforce the 1st Corps. And, as Doyle has pointed out, Holmes had gone so far as to designate Garland’s brigade as part of the reinforcements intended for commands east of the Mississippi.

In my opinion, those potential subtractions from the defacto 2nd Corps would not have left enough troops to organize an official 2nd Corps.

Intriguing stuff.