Ah, she might not despise him. She likes Aki well enough, though she would never admit it, and she doesn't really consider him stronger than her. He might just be a fluke, but she'd probably enjoy taunting and teasing Edgar.
Ayumi thinks all of Purple's Pokemon should come play in the snow! She'd love to be invited out for coffee or something. And, yay, shared interests! She loved coordinating, but she's much better at battling.