The expressions people would use around me are "¡Cállate! (Aquí) Yo soy el que habla." or "¡Te callas! Aquí sólo hablo yo".
"¡Cierra el hocico!" is a bit too long for saying anything else. I'd use it rather to end a discussion... this is what you would normally tell a child who is constantly grumbling back at you as you scold him.
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