It always puzzles me why Edward continues to be known as Earl of March after his father's death. Surely he immediately became Duke of York, and Regent, as well as in effect becoming Prince of Wales?
Another interesting quibble is that although Mortimer's Cross is usually stated to be a York v Lancaster fixture, Edward, the Rose of Rouen, was technically the accredited representative of Henry VI's government at this point.
Anyway - no one is sure exactly where Mortimer's Cross was fought, although it was obviously somewhere around Mortimer's Cross. It was a relatively small contest, essentially a defence of England from a predominantly Welsh force led by Jasper Tudor (aka Uncle Jasper) Earl of Pembroke, Owen - or Owain - Tudor, his father, and the Earl of Wiltshire and Ormond. The objective of the Tudor force - maybe for simplicity I should just go with the flow and call them Lancastrians - was undoubtedly to join up with Somerset's main army.
No one knows the details of what happened, except that Edward won, fairly decisively. Jasper Tudor and Wiltshire ran off and survived to fight another day but many of the other leading Lancastrians, including Owen Tudor, were taken off to Hereford and executed. A woman, generally described as mad, reportedly combed Owen's head, washed away the blood and lit over 100 candles around it. A point often missed is that she must have been a wealthy 'madwoman' as wax candles in this era did not come cheap.
Edward has been criticised for his ruthlessness, but the context must be borne in mind. He had recently lost his father, brother, uncle and cousin to Lancastrian violence and he undoubtedly wanted revenge. Although Warwick sometimes is seen as the more ruthless, Edward was no soft touch as he was later to prove on numerous occasions, not least in executing his own brother!
Edward and his army now moved east, with the intention of joining the Earl of Warwick and dealing with the main body of Lancastrians.
(I should mention that the battle is still re-enacted on a regular basis. See this link)