The key word is rebellion. The Yankees saw rebellion; the Confederacy saw separation. The Founding Fathers wanted separation; instead they got a war to forcefully bring them back into the Empire.
The Union was in no fear of being invaded. Yes, Gettysburg and several Maryland battles were in Yankee territory. However, Lee’s intent was to defeat the Union army and end the war. He was NOT after holding Yankee territory or winning over the people.
First, the war had been going for over a year when the Founders declared themselves independent. Second, there was no illusion that what they were doing was anything but rebellion. You find no Founding Father whining about how Britain had no legal right to fight them.
The Union was in no fear of being invaded.
The United States included ALL of the states. A hostile army in Virginia or Tennessee was just as much an invader as one in Pennsylvania or Maryland.