If you study the discussions at the Constitutonal Convention, you might question if the United States were ever really united. This is evidenced by the strained language in the Constitution concerning slavery.
Also, as I've mentioned in another post, I question if citizens were ever taught the idea of a constitutonally-limited power federal government.
You are correct that our union has been tenuous at times and that culturally the north and the south have been at times worlds apart. But there was a point of mutual interest that overrode all other considerations:
“...provide for the common defense...”
Every colony, even the most recalcitrant, recognized that they would be naked against the assault by their enemies without the united defense offered by the republic.
There is no strained language, or any other language that discusses slavery in the Constitution, until the 13 Amendment.