I wouldn't say it's out of her character for her to be emotional, nor do I think her action is "idiotic" on the face of it. Sylvanas likes to present a calm and collected exterior to her followers and soldiers, but I suspect her inner self isn't anywhere close to calm or collected - she's a maelstrom inside, and sometimes that inner self shows her true nature in unguarded moments. Her anger and despair are showcased in "Edge of Night" where she rages against the now-dead Arthas as well as the inert form of Bolvar, and then commits suicide as she feels there is nothing left for her. She loses composure again in "War Crimes," and yet again in the "Reunion" comic when confronted by her less-than-sympathetic sisters.
Delaryn, probably unintentionally or unknowingly, jabbed several of Sylvanas' proverbial buttons by reminding her of what she was, and what she had lost - her reaction, and the grand gesture that followed, reflect that rage pretty directly. I would say her action was calculated - albeit the product of some pretty dark calculus, but also honest to what she truly is.