Geez, you people are speedwatchers.
Azula was taught to control people through fear and thought it was the only way to keep them close. All of her problems are just due to her mother's neglect of her and her father's bad example. She just needed a change of perspective to show her how to truly connect to others. She isn't heartless or sociopathic, in fact she's so troubled by her mother's relationship with her that she starts hallucinating her. Spare the autist, she deserves better than that.