As I recollect, Lee maneuvered on Washington DC at Gettysburg and Sharpsburg. First Bull Run Beauregard tried to maneuver on Washington DC, by going around the right of Union forces.
Only because of loyal militia companies, and the disarming of disloyal militia companies was Lincoln ever inaugurated.
So yes, the southern pretended government did attempt to take over Washington, several times.
If the Army of Northern Va were to have captured DC, it would have been considered a tactical victory, not a strategic victory. The South wasn’t interested in taking and holding Northern territory. The whole point of secession was the opposite of that. I feel like I am talking to someone with less than a full deck when I post to you. Kind of a creepy feeling I get.