There are a few things that make this poem so Rita Dove. The main thing is the content. Much of her work focuses on individuals in relationship to their families. She looks closely at growing up and how that change affects relationships.
She also really enjoys giving a modern spin to older situations, whether it's Greek mythology or history in general. In another poem, she gives Beethoven a contemporary voice as he travels. Plus, this isn't the only time she has tackled the whole Persephone-Demeter-Hades dynamic. Check out "Hades' Pitch" for another example.
Finally, Dove uses a lot of sneaky formalism. She writes lots of sonnets, but does so with lots of enjambments, internal and slant rhyming and a lack of regular meter. Think of it as ballroom dance (and check out our "Best of the Web" for a glimpse at Dove actually dancing): there are formal steps, but beyond that, it's all about how she riffs off of them.