If this is her typical pattern of behaviour, -like personality types that love the adrenaline rush from being angry- this lady could be one of them.
Its the type of attitude that cognitive behavioural therapy could help with.
However, don't fuel the fire, rather leave it to burn out, as feeding her anger would give her a further buzz.
I like your attitude, your response so far is spot on. She is a sad lady, but her choices in life have made her the way she is, nothing else. No excuses.
Perhaps this is of any help:
I used to be like that in my early 20s and the only thing that helped me to snap out of this awful behaviour was being constantly ignored by my "targets" and massively growled at to "grow up" when once again I had over done it. I am forever grateful to those people... hadn't they been so persistent I probably would have learned this very important lesson much later in life. Most likely I would have embarrassed myself in front of e.g work colleagues or worse instead of "only" my fellow students.
Hence ignore her as long as you can if it gets too much tell her to "grow up"!! It doesn't matter how old she is as I have met a few adults (> 40y) with this kind of behaviour. I am always the one to empathise but do "lose my temper" when I see fit (after all I was there myself... ).