There should be no guilt when your DD says that she hates you - it is obviously emotional manipulation and you should treat it as such. I would tell her casually that it was all right that she hated me or that it was not a problem or even that "I hate myself sometimes too, so it is nothing new!".
I set very high expectations on behavior, especially when out in public places and expect my child to not create problems for others who have a right to conduct their business without being subjected to emotional drama from others. If this happened, it would be the last time that my child would go to a library or a public place to hang out, work etc. The child has to prove to me over a long period of time that they can be trusted to behave without having meltdowns before I take her out to such a setting again.
As for how to defuse the situation when this happens, I would try distraction. That is the only way that I can manage an emotional situation. This behavior may be the result of anxiety, stress, tiredness, hunger etc in addition to the puberty hormones that HK pointed out.
