Confederate leaders hoped that a victory in union territory would win support from?

Answer 1

Presumably you are referring to the South's efforts to obtain an alliance with major European powers like Britain or France. Like the Colonial victory at the battle of Saratoga, the South hoped that more victories against the North would bring those countries into the war on the side of the South.

However, that wasn't really the main goal when the Confederacy's forces finally moved to attack the North on its own territory. The reason Southern leaders wanted to launch an offensive upon the North was to take some of the pressure off the South itself.

Most of the early Civil War was fought in the South, especially Virginia. General Lee's invasion of the North, which culminated in the Battle of Gettysburg, was an attempt to draw Union forces away from the South and to cause damage on the North. The hope was that with Lee and his "invincible" armies rampaging through Pennsylvania and New York, Northern morale would plummet, and Lincoln would be forced to make peace with the Confederacy.

However, Lee's defeat at Gettysburg put an early end to the campaign. Lee was forced to return to Virginia, and the remainder of the war was largely fought on Southern soil.