By what orders was Stuart suppose to attack the back side of the Union center on the 3rd day at Gettysburg.
I believe it is assumed he would have seen the opportunity and just done it.
Every book on Gettysburg that I've read, by Sears and Trudeau and Wert, detail how Lee ordered Stuart to support the infantry charge by riding around the Union right flank and down the Baltimore Pike in the Union rear. The attack was as big a folly as Pickett's attack was because Stuart's men were tired and their mounts worn out from his joy ride through Pennsylvania. Union cavalry were able to repulse Stuart's men, though stupid leadership on the part of Kilpatrick led to heavier Union casualties than should have been necessary.