My interest in the Civil War is about the soldiers who fought in Tennessee units. Military science or dissecting battles is not my cup of tea. Having said that, I have done a little researching re: your questions.
Go to the website battleofnashville.com and the article "Gunships vs. Cavalry". The author states that the 10th TN CAV was attached to Brig. Gen. James R. Chalmers Escort Co., were on the Yankees Right Flank on Charlotte Pike (West Nashville), and moved to Murfreesboro 13 Dec 1864.

The area mentioned is Kelley's Point Battlefield which is in Bells Bend of the Cumberland River.
Maybe someone with more knowledge of the Battle of Nashville will be able to help you more.