The 2nd/15th KY Cavalry was not at Parker's Crossroads because the regiment did not exist at that time. Let me detail the history of Woodward and the units he was involved with for you so you can better understand this. This is from the KY Adjutant General's books by the way.
1) June/July 1861 - Woodward, living in Hopkinsville, KY, forms the Oak Grove Rangers. Oak Grove is a town on the TN/KY border - I live about 5 miles from it today.
2) The Oak Grove Rangers expands into a three company battalion and becomes part of the 1st Kentucky Cavalry under Ben Helm. This is a one year regiment that dissolved in the mid-Summer of 1862. They reorganized for the war but Woodward and some of his men left the unit.
3) Woodward heads back to the Hopkinsville area to recruit what would become Woodward's Kentucky Battalion - July/August, 1862. This two company battalion joins with the newly forming 10th Kentucky Partisan Rangers (under Adam Rankin Johnson) and attacks and captures Clarksville, TN in August. Woodward then takes most of the men to attack Dover but is repulsed there. In September, a Union brigade retakes Clarksville from Woodward.
4) Woodward's battalion joins Forrest's command for the West Tennessee/Kentucky raid in December 1862. This raid destroys the Mobile and Ohio Railroad in these states while Earl Van Dorn's raid took Holly Springs, Mississippi. These raids forced U.S. Grant to abandon his first attempt to take Vicksburg.
5) In January 1863, Woodward begins recruiting what would become his 2nd Kentucky Cavalry. There was already a 2nd Kentucky Cavalry raised by John Hunt Morgan and this caused confusion. The number 15th Kentucky Cavalry came after the war and was done by the Kentucky State Adjutant General. Thus, there were the 2nd Kentucky Cavalry (Morgan's/Duke's) and the 2nd Kentucky Cavalry (Woodward's). This regiment would serve for the rest of the war but Woodward was cashiered as its colonel as he did not file any battle reports among other problems. You have to be very careful to not confuse these two units which at least one author that I know of has done - despite me correcting him before his book came out. He has a certain soldier of the 2nd Kentucky Cavalry (Woodward's) being at Stones River and Parker's Crossroads in December 1862 - except both battles were fought the same day and quite far apart.
6) Woodward was back in Kentucky in 1864 and with some new command attacked Hopkinsville and was killed riding into town - supposedly drunk.
Hope this helps.