Don't let her actions, if she still has you down as emergency contact, dictate what you want to do; you tell the emergency people who call you are not her contact; it's not like she's a relative. Could be it takes a literal wake up call like that from someone else for her to understand. E-mails and constant complains or threats, etc. can be ignored or imagined away but having the ER say, "try again, that person doesn't want anything to do with you" can't be ignored and gotten around?

For me, that sort of comeuppance would make it feel more "fair".