"Both Tennessee Union and Confederate Regimental designations tend to be conflicting and on some instances duplicated. For example, by the time Tennessee Adjutant General Alvan Gillem assumed his office there were a 1st East Tennessee Cavalry, 1st West Tennessee Cavalry and a 1st Middle Tennessee Cavalry all sometimes known as the 1st Tennessee Cavalry. On assuming office, he redesigned many of the regiments to avoid further confusion.

Lt. Milton W. Hardy of the 7th Tennessee was, in the fall of 1863, authorized by Tennessee Military Governor, later President, Andrew Johnson, to recruit the 15th Tennessee Cavalry. He first opened a recruiting station at Paducah, KY and recruited a number of soldiers from the Unionist Refugees then present in the city. Later he took the men he had managed to recruit and opened a recruiting station near Reynoldsburg, TN on the Tennessee River and again began recruiting activity. It was during this time that Hardy was killed in action and the two companies he had recruited were absorbed into the 2nd Tennessee Mounted Infantry. I get the impression however that the unit your interested in was from East Tennessee.

Also in late 1863 Federal General A. Burnside authorized the recruitment of the 12th TN Cav, also known as the 13th. This was an East Tennessee regiment and likely the one your interested in.

Also organized in this time was the 14th Cavalry, also known as the 13th. This unit was decimated at Ft. Pillow in West Tennessee.
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Tennesseeans in the Civil War Part 2 reports that there were the following McQueens that served in Tennessee Union Regiments
13th Tennessee Cavalry
Co. E (generally from Greene and Johnson Counties)
Private Godfrey F.
Corporal James K.
1st Sergeant Samuel E.

Co. G (generally men from Carter County)
Private Alexander H
William M. 1st Lieutenant

Co. L (men from other states and upper East TN Counties)
Private John G.

The Tennessee 1890 Civil War Veterans Census reports entries for
Alex H. (Washington County) as a Private of Co. G 13th TN Cav who was then living near the Flourville Post Office
Samuel E. (Johnson County) who was a Sergeant in Co. E 13th TN Cav who was then living near the Head of Laural Post Office."

(...)

Bill Morris
Senior Vice Department Commander
Department of Michigan
Sons of Union Veterans of the Civil War

Alexander moved to Texas with his children and father about 1880. Nothing supports the idea that Alexander would move back to TN and leave his children in TX with his father. His daughter married in TX in 1892, so it's unlikely that Alexander had returned to TN before then.