Oiveyizmir (my apologies if I spelled your name wrong): In all the debates going on here, I feel like you’ve been forgotten.
First of all, how is the situation? Has it changed at all? Has it gotten better? Worse? Have you found out anything more? You mentioned that you were considering speaking to your neighbor or having your wife speak to his wife? Did either of you do that in the end?
Second of all, I really want to commend you for the way that you have been handling the situation. It must be a terrifying situation to be in. I know that personally, it gets me very nervous when I hear people fighting. And I get really upset when I hear family members being abusive to each other (even if it’s “only verbal” as you put it).
It must have been very difficult for you to refrain from calling the police when your Rav told you that he will handle the situation and that it would be (halachically) problematic for you to call the police. And when the fighting and screaming continued, it must have been really hard for you to restrain yourself.
You are right for being cautious about calling the police, but you are also right for being concerned about the situation and realizing that you should try to do whatever you can to help and not just say, “well, I called my Rav, and now I can wash my hands from the situation.”
If you still hear fighting, I would recommend that you call your Rav and find out if he is in fact doing anything. Tell him about your concerns, and tell him that the fighting is still going on, and ask him what he is doing about it. You mentioned that he is a well-respected Rav in the community, so the first step is to find out if he is really taking care of it.
But if his answer leaves you unsatisfied, then you should speak to someone else. Find another well-respected Rav/Poseik and ask him what to do. Perhaps you should speak to your neighbor yourself or have your wife speak to his wife, as you mentioned. If you are really concerned that someone is being abused (even if it’s “only” verbal), you definitely should try to do whatever you can, but make sure that you act rationally and don’t act on your emotions. Doing so could exacerbate the situation instead of helping in addition to the possible halachic issues involved.
Remember that as a Frum Jew, the most important thing to remember is not to violate any halachos. If something is against halacha, then it doesn’t help. If you are unsure if the psak you are given is correct, ask a bigger Poseik. But don’t do something against halacha.
Hatzlacha Rabba! I hope that the situation improves and that Hashem gives you the Siyata Dishmaya and the wisdom to act correctly.