Layla - an aide from the nearby Pokémon nursery - shows up looking for the two squabbling Pokémon. She brings Rufflet and Vullaby - along with Ash, Iris and Cilan - back to the nursery with her.

This is found on the Paniola Ranch. You will be given an egg the first time you go to the Pokemon Nursery. This egg will hatch into Eevee. Found in Aether House after you defeat the Elite Four.