Unfortunately I've injured my dominant hand and wrist and cannot type very well right now. Ugh. But I will try. It may not be to the degree of my usual posts. Waiting for the ibuprofen to kick in and my DH just went to to try to find me a splint.
I've said from the beginning of this thread that I think that life for a dog with working or otherwise low key people is probably ok for most dogs. It is THIS dog we're talking about, though. The OP asked for ideas and solutions because his behavior is problematic and they have come to a crossroads about how to deal with it. It's not a stretch to say that literally this problem could ultimately cost the dog his life. I take that seriously. I have also spent most of my life working with and training dogs so I well understand the sometimes extreme challenges they can present as well as the joy that a well behaved dog can bring - and everything in between. If I can share that information to help people and dogs, then I will.
Unfortunately the information is not always easy to hear. And people have lots of ways of dealing with dogs and dog behavior. Some are ideal, some are fine, some border on inhumanity, while still others are downright cruel, depending on each given dog and situation.
There are laws on how to treat dogs, but they often deal with just a physical state - food, shelter, medical care. There aren't a lot of laws on whether something that's legally ok to do is necessarily humane. We have humane and other societies, which were started more than a century ago in response to widespread cruelty, who work tirelessly to try to educate people so dogs and other pets and animals will have a better quality of life as people are educated to their needs. But not everyone follows their recommendations and it is not required to do so. It becomes a choice. And this is where it gets tricky.
Not unlike parenting advice, dog advice can, not surprisingly, lead to all kinds of disagreements.
So the OP has two dogs, one of whom seems perfectly fine with life as is. Then we have the other dog who is acting out his displeasure with life as is, to the point where he has become destructive, a nuisance, and even developed some potentially dangerous behaviors such as aggression towards other dogs and unreliability around people.
These are problems of socialization and training. Not every dog has these. But some do, and this dog is one of them.
I'm not going to make any rash judgements or recommendations that all dogs have to have nine walks a day and each must be three miles or greater. No. That is great if it happens (such fortunate dogs!), but most people who own dogs are not going to do that. Most dogs, however, are going to share part of their day with their human pack and have some sort of vigorous mental and physical stimulation at least daily or several times per week, and that's good enough for most dogs. Unfortunately, some dogs don't have even that, especially when their behavior has deteriorated to the point that they've become unpleasant to be around. And this is, if I'm understating correctly, what we are seeing here.
So now we have a dog whose needs are not being met in his living situation, his behavior is problematic, and there needs to be a solution found. Many dog enthusiasts have said, hey, I recognize that problem, a dog like a Labrador has instincts to work, and if he's woefully bored, then a good solution to the problem is simply to increase his physical exertion so he can drain some of the excess energy he has. It wouldn't have to be extreme, maybe just some daily play in the back yard, and you don't even have to do it yourself, you can actually pay to have someone else to do it! As long as it's done, that's the big point. That is a solution that's both complassionate to the dog's innate needs and humane. Win-win for everyone.
That is not going to be the first intervention, however. First is going to be to give the dog medication that alters his brain chemistry. And up for consideration is caging him in a relatively small crate for the ten hours a day that the OP is gone. Still humane and compassionate? Maybe, maybe not, depending on how you look at it. But wait, best idea yet, how about placing a collar that delivers a painful electric shock if he barks? Humane and compassionate?

No, it's not. Would the latter even cross into the territory of inhumane and cruel? Yes, quite possibly. Why, though, when these collars are perfectly legal and even trainers sometimes recommend solutions like this? Well, let's think about it.
You have a dog who has not been trained and socialized properly. Yes, same owner has another dog who seems to be perfectly fine, but this dog is not, so this dog's needs have seemingly not been met in this situation. And instead of starting with logical, humane solutions such as the giving of time and stimulation, which there is little time for, we go down the continuum to the method that is perhaps easier, but headed down a questionable path. Why do vets and trainers go along with these types of things if there are even questions about their being humane? Well, because vets and trainers know that, should these problems not be solved, the dog will likely end up in a bad situation, as in a shelter, or worse, euthanized if the bad behavior is past a point that anyone can work with it OR something bad happens, like a bite. So they feel that this type of solution is better than none at all. That's why. It doesn't make it the BEST solution, necessarily, just a solution that's legal and acceptable. Vets and trainers can offer other recommendations, but there are no guarantees that anyone will follow them. People aren't always willing or able to put the time in that it takes to have a dog healthy of mind and spirit. And honestly, lots of people don't really care, either.
For the record, as I've said earlier, I do think that the OP is not someone who doesn't care. I do think she's got a very busy life (many of us have been there, for sure) and the dog's special needs here, while not intended to be so, have become overwhelming. But we have to remember dogs are living, breathing, thinking, feeling beings who aren't statues who sit there looking pretty endlessly. They have needs. They just can't express them verbally to us. (Although they will express them non-verbally.) And because they're lower on the food chain, we sometimes think it's ok to overlook their needs. People who really care about their dogs' well-being take steps to have and keep a dog healthy, trained, socialized, and well-behaved. This is what we're seeing here with all the people who may not necessarily want to be out in the cold running with their dog or otherwise helping them get some exercise, but who do anyway. Or go out and kick them a ball, play with them inside, develop tricks and games just to curb some of the boredom, etc.
I've "known" The Mystery Machine here for many years, since her high maintenance dog(s) were young. I am very confident using her as an example of someone who has gone above and beyond in taking her commitment to her dogs very seriously. As she's mentioned here, she's worked tirelessly to curb her dogs' behavior, especially with one, and now that dog is nearing the end of it's natural life and has always enjoyed a great life with her despite her often very difficult life circumstances. (Many moves, family issues, MAJOR health issues, etc.) I'll say it here publicly, TMM, you have my utmost respect. Your dogs can't say it, so I'll say it for them. THANK YOU FOR ALL YOU'VE DONE, ALL YOUR HARD WORK AND DEVOTION TO US!

I do believe there'll be special rewards for you some day. Christine is another with her dogs. Tolzkin. And many others here. Awesome dog owners and great examples. Thank you.