I agree that you need to have a protective order in place. That should be your first step.
As far as suing for emotional distress, you would need to establish a number of things. To prove a cause of action for intentional infliction of emotional distress, the neighbors must have intended to cause emotional distress or were reckless in causing emotional distress.
Second, you would need to show that the conduct was outrageous. The law will not recognize a simple threats, insult or emotional injury without some "plus factor.” This means that the conduct has to be unconscionable. An example would be that your wife suffered from emotional issues already that your neighbor knew about before threatening to kill her and her family. That would probably be a good plus factor.
Third, you will need to show that you or your wife suffered severe emotional distress. Generally speaking, the distress suffered must be what a "reasonable person" would undergo given the circumstances. Also, bodily harm is not a requirement - mental harm may be sufficient. That being said, the courts will scrutinize the outrageous conduct if there hasn’t been any physical harm. You would also need to show that the damage was actually and proximately caused by your neighbor’s conduct.
Without knowing more, its' not possible to say whether you have a good cause of action. You should speak with an attorney. And make sure you get a TRO immediately.
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Under the circumstances you describe I believe you meet all the requirements for such a suit as outlined by my colleague. That however is just my opinion. You need to find a lawyer who's going to step up for you and he/she is the first person that needs convincing.