You may find the Compiled Service Records of Volunteer Union Soldiers Who Served in Organizations From the State of Alabama [or Tennessee], 1st Alabama and Tennessee Independent Vidette Cavalry to be helpful in sorting out your relatives who may have served in the regiment.
I have found these records listed under Tennessee and Alabama Units. In any event, there are several soldiers named Warren and Cox in the Regiment. Contrary to popular belief the 1st Alabama Cavalry was not the only Union Regiment from Alabama. The majority of the men of the 1st Alabama and Tennessee Independent Vidette Cavalry were from Alabama. There were also significant numbers of soldiers from Tennessee and to a lesser extent Georgia.
If you do not have access to the Compiled Service Records, there is a book that was published in 1995 by Mountain Press, compiled by Johnny L.T.N. Potter that has a good synopsis of the records. The name of the book is "First Tennessee & Alabama Independent Vidette Cavalry Roster, Companies A,B,C,D,E,F