As for the "I hate you" line, my stock response is, "that's alright, you're feeling X because Y. I'll always love you, and nothing you ever do will change that." It's a covert way to succinctly communicate that the underlying emotional need has been heard while reframing the incident around love. In any given incident, it might not be effective at tamping down hysteria but, used consistently, helps with the faux hurt feelings.
As to the hysteria, don't feel that you have to explain or justify yourself in the moment. The rationality train has flown over a cliff at that point. I think of my job during meltdowns as containment, then discipline, then discussion.
