That weird Hillary laugh...
I don't think Hillary's crazy, wide-open-mouth laugh is hard to explain. If I remember correctly, she was known as the "Ice Maiden" in high school. And, certainly, smiling never came naturally to her, as footage of her from the 90s proves (at one time, she never did it).
Since then, she has had handlers tell her she has to smile and laugh to seem more appealing, but it's all put on. As a consequence, she's a bit like the people on "Third Rock from the Sun" when they try to imitate human behavior. It all looks very weird and artificial, and she often doesn't do it in a contextually proper way because it is phony.
It's as when a sociopath has to think, in order to seem genuine, "How would a normal person react in this situation?" And Clinton does seem quite sociopathic (this isn't to say she's a full-blown sociopath).