"But the problem is that the various republican movements want to conquer a sovereign nation that does not want to be conquered by them. "
Do you know this or is it an assumption?

We know this Jim because had the North wanted to be united with the South they would never have ceceded in the first place, I believe they were actually "United" for about three days from the 6th December 1922 (Notification of the wish to cecede being sent on the 7th December, 1922).