Your ancestor's unit was Company “K” of Randolph County, the "Louina Guards". It captains were:

Alfred C. Wood. Appointed Major May 21, 1862, to rank May 12, 1862.

George W. Taylor. Promoted Captain [June 7,] 1862, to rank May 28, 1862. Wounded at Frazier’s Farm, Virginia, June 30, 1862. Appointed Major August 25, 1863, to rank May 26, 1863.

W. A. J. Swan. Promoted Captain on September 4, 1863, to rank May 26, 1863. Wounded and disabled July 2, 1863, at Gettysburg, Pennsylvania. Elected Tax Collector of Randolph County, Alabama; resigned December 14, 1863.

Gustavus F. Weaver. Promoted Captain [January 15,] 1864, to rank December 14, 1863. Wounded and disabled at the Wilderness, Virginia, May 6, 1864.

Accepted by the governor of Alabama on July 22, 1861, the company mustered August 1, 1861, at Louina, Alabama. A roster of officers and men entering Confederate service was dated September 5, 1861, Camp Johnston, Alabama.

The other company from the 12th Alabama was Company “B” of Coosa County, the "Coosa Independents". There is a book by Wayne Wood on this command called the Marble Valley Boys. It captains were:

Joseph H. Bradford. Resigned December 31, 1861.

John C. Goodgame. Elected Captain on January 7, 1862. Reelected April 29, 1862. Appointed Major [September 10,] 1862, to rank June 1, 1862.

Henry W. Cox. Wounded and captured near Boonsboro, Maryland, on September 14, 1862. Promoted Captain September 25, 1862, to rank June 1, 1862. Exchanged at Aiken’s Landing, Virginia, October 19, 1862. Wounded at Chancellorsville, Virginia, May 3, 1863; died there May 9, 1863. [DAB3:407]

Patrick Thomas. Promoted Captain during [June 21,] 1863 to rank May 9, 1863. Wounded at [Spotsylvania Courthouse, Virginia, May 10, 1864,] Winchester, Virginia, September 19, 1864, and [Petersburg, Virginia, April 2,] 1865. [Died at Danville, Virginia, after April 8, 1865.]

Organized at Wetumpka, Alabama, as the “Coosa Volunteers”, this company served from February 28, 1861, to April 5, 1861, at Fort Morgan, Alabama. Members mustered in Confederate service at Camp Bradford, Coosa County, Alabama, June 17, 1861.

As you can see, Owen's Dictionary of Alabama Biography includes a sketch of Capt. Cox, so you can check his family line to see if he is related.

Another minor point: the two battles took place on the same day, but the 14th Alabama was part of Wilcox's Brigade and fought at Salem Church, near Fredericksburg. These men fought a rear guard action which saved Lee's army from destruction. The 12th Alabama belonged to Rodes' Brigade, which struck the Federal right with Jackson's Corps and lost heavily on May 3rd. The two regiments were quite some distance apart from one another that day, serving in different commands. The name similarity is just coincidence.