Firstly i'm sorry you've been through this and had to go to the trouble to find a fix.
Well i have a Jack Russell and yes sometimes he barks. If it really is a problem with your neighbour and there has been no resolve for two years then here's my advice. Take it or leave it... it's a different approach.
I don't know type of dog or people involved but here goes... When my Charlie barks it's for two reasons, he's waiting for me to get my welllies on to take him for a walk or the garden thief scrotes are having a look at what they can pinch through the fence. Whatever type of people they are, if the dog is that persistently barking... he's bored, really really bored. Lets say this dog belonged to your friend, not the neighbours who you are annoyed with, a nice long term friend. How would you approach it? I get that it's an inconsiderate and frustrating situation but stay with me. Give them a knock and if you dont know them that well, introduce yourself and ask if they have a min. Explain a bit about yourself and then be honest. Your life is really affected by their dogs constant barking, you're worried about him too and in fact it's making you unhappy.... BUT you want to help. (You can make all the complaints in the world, do all the mean suggestions etc but all you really want is to resolve this in a compromised way, right?) They're used to it, could have been brought up with nosiey dogs and with the new puppy around, you dont want this behaviour to be learned and become twice the problem! So, take some dog biscuits round and offer to take him for a walk, believe me if they are decent humans they will be so humiliated it will humble them. Shame them. Don't judge, shame.
I was doing 15 hours shifts at one point and my neighbour offered to take Charlie out because he was becoming a nuisance. I had no idea, i felt so bad. I put all my energy into work. I now take him out at silly o'clock before i go to work. They were right, he needed to be taken better care of, i took my eye off the ball for a short time which wasn't fair on them or him. TBH, without this intervention i wouldn't have known how bad it was and if they hadn't of said anything, it would have condoned the situation.
Sincerely i hope you find a solution, best of luck.
I used to work nights (never again) and the noise of home alone dogs etc used to keep me awake sometimes, so I know how annoying it can be.
