In hindsight we can say that the road to disunion began with American independence. Do you see anyway disunion could have been avoided by pursuing a different policy at any time between 1776 and 1861? Or was it inevitable?

While this question depends largely on one's opinion, I think that disunion could have been avoided if the new nation immediately freed all the slaves after the American Revolution. It could have taken advantage of the spirit of unity within the colonies directly after independence. There were few slaves in 1783 compared to what there would be in 1860, when the amount of money tied either directly or indirectly to slavery would reach millions of dollars. As the number of slaves increased in the United States and agriculture related to slavery became more profitable, it became less likely that slave owners would react positively to the freeing of slaves.
If this happened, the newly freed slaves could have stayed in the United States, living side-by-side with whites, or perhaps settling the sparsely populated West. Civil rights for former slaves would have been a struggle even in this alternate history.
Given this answer, one could say that disunion began at the founding of the colonies and that it was inevitable. Slavery made the North and South culturally different, and it would take the Civil War to forge a common inseparable bond between the two regions, the bond being the Constitution's supremacy and the ultimate abolition of slavery.