[…] his glittering terriblecarriage […] (5-6)
This quick, vivid description juxtaposes the attraction of lust to our eyes, while still making us uneasy. Dove enjambs the line to let those two words sink into our minds side by side. Lust can make things glitter, sure, but it can also be terrible news.
[…] he claimed his due. (6)
Hades doesn't propose, doesn't persuade, doesn't even buy her dinner. Instead, he "claims his due." What makes lust a pale shadow of love is its nasty habit of transforming people into objects. In Hades's mind, Persephone is property that he is owed. Yuck.
This is how easily the pitopens. This is how one foot sinks into the ground. (13-14)
Lust is often pictured as a slippery slope to trouble. In Persephone's case, it's that little curiosity, the need to possess that one flower (which, oh by the way, is named after a hunky guy), that leads to her downfall.