The resolution, for Barbara Frietchie, is that it is better to sacrifice one's life to restore order.
Whittier asserts that nature will triumph over manmade chaos.
To Barbara Frietchie, the flag, with its symbolic representation of unity and order, is worth more than life itself.
Thus, the idea of a unified orderly existence is the priority. Whittier implies that the chaos of nature is temporary, and he strongly disapproves of anything that would disturb its peace.
Therefore, the Union flag provides a sense of normalcy after the storm just as calm winds and receding waters represent Nature's way of restoring order.
Whittier is saying that violence isn't the natural order of things, and the reader may believe that Whittier is speaking beyond the presumed moral superiority of the Union.
He is affirming the importance of Nature over all creatures.