Lyric discussion by tragicweek 

It does sound like a civil war era interracial relationship that ended before the song's narration.

'Were hanging in the shadow of your family tree Your haunted heart and me Brought down by an old idea whose time has come'

They got hanged

'Were laying in the shadow of your family tree Your haunted heart and me Brought down by an old idea whose time has come'

Being prepared for burial

'And now we’ll gather in the shadow of your family tree In haunted harmony Brought down by an old idea whose time has come'

Then being buried.

'And in the shadow of the valley of your family tree' is an allusion to Psalms 23, "though I may walk through the shadow of the valley of death," a line that is used as a symbol of God's protection from evil, but in this case alludes to the Family Tree as death.

With that in mind this song becomes less about the couple and more about the Family Tree, which could be interpreted literally to mean that they were hanged from tree that the family has lived around for decades and then were buried at it's roots to become one of the hundred bodies buried under the tree that have become a fertilizer for the tree that will keep the Tree healthy and make sure it can still be used to hang couples from and "keep them young"

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