And the people she was out partying with should be downright ashamed of themselves too
I doubt they knew about the neglect. I suspect that most people out partying with a parent would assume that the parent had made suitable arrangements for childcare.
I honestly don't understand why she was charged with manslaughter and not murder
The prosecution has to show beyond reasonable doubt that she intended to kill or cause grievous bodily harm to get a murder conviction. I can't see anything in the press that indicates an intent to kill. Yes, it should have been obvious that leaving her child alone for 6 days would lead to its death but that is not enough on its own to establish an intent to kill. On the information we've got I would say this is clearly a case of gross negligence manslaughter.