No solution to offer, but my sympathies.
We have had problems with our neighbor on one side in the past, but things have been pretty calm for the past year or so. Their dog is maybe 2 years old. Really nice dog, but over the past year or so he has started barking a lot. They let him out in their yard for maybe 20 minutes at a time, during which he is apt to bark constantly. At what, I’m not sure. But it is annoying. And I anticipate it will be even more so when temperatures rise and we want to have our windows open. It surprises me that it doesn’t bother them as well.
Our situation is the opposite of yours. He does not bark when I am outside. Probably because I talk to him. And he shuts up when I tell him to. He really is a nice dog. I think he is just bored. I can open the door and yell at him to shut up, and he will. But then he will start up again a minute later. And I never hear his owners tell him to shut up.
We have a dog as well. But we don’t leave her in the yard when we are not home. When we hear her bark, we tell her to shut up. If she doesn’t, we bring her inside. She gets most of her exercise from walks/runs anyway, and mainly goes outside just to do her business. If we are inside, that is where she prefers to be.
But, like I said, otherwise things are going pretty well with these neighbors who have been problemmatic in the past. So we are hesitant to make this into a big deal. Just another way you don’t appreciate good neighbors until you have bad ones.
In my experience, your first step is to talk to the owners. Maybe that will be successful. With my previous dog, he was always very quiet when we were at home. We took to leaving him out when we were gone, until our neighbor told us he would bark constantly. We had no idea - it seemed so out of character for him. But we stopped leaving him out when we were not at home.
Unfortunately, I feel a good many folk will just say “Tough. You want quiet, move to the country.” And then you will be in the same situation, with pissed off neighbors.
Your next step is to contact the cops. They will let you know what nuisance restrictions there are - if any. It may be illegal during the night, but not at day. Or it may require continuous barking for a certain time. They might talk to the neighbors, which again, will have the neighbors hate you. But they will require that you swear out a complaint before they do anything beyond that. And you will have to decide if you want to go to such lengths.
Like I said, you have my sympathy.