There have been many occasions when I wished that my neighbors would make their screaming children shut up. But there is no law that requires that.
My neighbors also had a motorcycle, I would take dog barking any day.
I think my real issue is that IF there is no law about noise in your area, than dogs are ALLOWED to bark during the daytime. Most places do get a bit hairy about barking after dark, and I think that you mentioned that they bring the dogs in at night.
My dogs are outside all day. Sometimes they do bark. I put privacy fence on the one side and am awaiting my tax return to complete the other side. We do what we can, but women living alone whether single or divorced generally do not have a ton of money, time, or anything else (including healthy young bodies to help move the junk out of the yard).
So that kind of rubbed me the wrong way as well. The OP was pre-judging the woman, by saying that she worked at home (so obviously she has plenty of time), that she was attention seeking (junk), and that she was divorced -- not sure if that was just info, and that she is not trying -- eventhough she is not just ignoring the barking, but coming out and trying to get the dog to quiet down.
It is possible, that she can get more work done if the dog is in the yard. Sometimes if you have a hyper dog, that is pacing back and fourth and whining, it is hard to concentrate on what you are doing, so she puts the dog out. That isn't a problem. People who go to work outside of their home are not with the dog 24/7. And some dogs are a royal pain when they are crated and you are there.
I think the woman is aware that her dog is a nuisance, but she may not understand how annoying her dog is to others, and she may be totally at a loss as to how to manage it. Personnally, I think putting the dog in a different room with a baby gate and a chew toy, if it is bothering her, and going out with the dog when it has to potty could make quite a difference.
Not every dog needs to have several walks around the block every day. That You take your dog for walks is great, Good job! I do not take all my dogs for walks everyday, and frankly, some of them could care less. Some of them LIKE to stay at home. The majority of the them get excited when I get the leash to take one for a walk. But ALL of them are just as happy to get in the SUV and come HOME. (I have to drive my dogs into town to walk them.)
There may be other reasons she does not take the dog OUT. There may be dog aggression or people aggression issues that the woman has no clue how to manage. Or she may have never taught the dog to walk on a lead and the dog is very unmanageable. Or she may have a physical/health problem. As for the aggression issues, I would rather a novice owner keep the animal home, than to have the dog attack another dog or person. If it is a training issue (very likely), well at some point we all have to face the very real fact that what is important to some of us, is not important to others.
My hope for the dog is that it has enough redeeming qualities that the owner is willing to keep it throughout its lifetime. There is not much of a market for huge untrained dogs, and its chances in a shelter are pretty slim.
If this really bothered me a lot, I would write a very nice letter to the woman with kind suggestions and alternatives to leaving the dog unattended outside. Just a couple of suggestions and the card of your dog trainer should do it. I would not threaten, and I would sign it.
I am not so afraid of retaliation, not if my letter comes across as positive, helpful, and non-judgemental. Within a couple of weeks, you will know if she is trying and if she is not and there is a law in your area, you should go further and call the law. Sometimes people do not think that the problem is serious until a uniform shows up.
But your neighbor should know who has an issue with their dog. especially if she can only afford to put privacy fence up along one side of the yard.