The short, easy answer is to give up your pets and live your life more like what most other people would prefer. That is a totally acceptable decision. Here is a long answer and one that I, a city dweller, primarily adhere to:
Dual pane windows do a lot for soundproofing, but, holy cow, are they expensive. Mass stops sound, so the thicker the plywood, the more sound it will stop. There are specially made materials that stop sound, but they are expensive. When I was in an apartment, my neighbors were noisy, so I hung a blanket on the wall. It made kind of a big difference.
Temperature control can be done. Dual pain windows help and covering the windows from the outside helps. Use the best quality insulation you can as you have a very limited space and that limits the amount of insulation you can put up. Some places have an outlet placed at the end of the parking spaces to plug in your block heater during the winter. Perhaps that is available and you could plug in air conditioning? I'm planning on getting AC that runs only on my solar, but that is an expensive ordeal and may not work anyway. A lot of things need to line up to make AC work on solar and having that much solar on your roof is noticeable. If you can park in shade and use a fan, you can do a lot to keep your pets safe and comfortable. Perhaps on the hottest of days doggie day care may be needed, but the rest of the time it would be fine.
I get out a lot. As a result I have had more than my fair share of confrontations. If you have a pet and get out a lot, you are going to have problems. Every once in a while law enforcement is called on me. Because I've never, ever been a problem, I've never gotten in trouble. My dogs have always had the best behaviors and that makes a huge difference. Yes, I've made mistakes as have my dogs, but anyone who expects perfection is too onerous and isn't taken seriously. Cops have better things to do than bother a hard working man and his exceptionally well behaved dog.
I have a CCW. That means I'm one of the good guys and that makes a difference. If I had a rap sheet, had a warrant for unpaid fines, and acted like a dysfunctional jerk, I wouldn't have what I have now. If you are one of the good guys/gals, then do things that demonstrate that. Don't brag about yourself, but tactfully display who you are. Good people are given more leeway. Bad people not so much. You will need to be given leeway if you are to have two large dogs in a van.
I'm a one-dog dude. As competent as I am, I won't have two dogs. Too constricting. One dog is a lot of work and two dogs is more work than I care to do. Having one dog makes a huge difference. I've seen vandwellers with more than one dog, but I won't make that much of a sacrifice.
Mine is a 45 pound dog. I like the size. Any bigger and having them around becomes surprisingly more difficult. Small dogs are much easier! Am seriously considering a small (20 pound) dog for my next partner in crime. It wouldn't be my first choice, but not a bad one.
No matter what you like to have in your life, someone will have a problem with it. I largely do what I want as long as I'm not hurting anyone. Being courteous and making as big of an effort as you can to minimize your impact on others goes a long way. I'm amazed at what I get away with when I don't inconvenience anyone or cause harm to my environment.
If work allows you to go out and let the dogs out every 2 to 4 hours, that makes a big difference. If you can limit work to 4-6 hours a day, you could simply go to work then let the dogs out when you get off. Living without bills and without a ton of stuff will allow you to be free from a self-imposed, financial prison and will better allow you to have the freedoms you want with your pets.
I had a job where I said I would work for them, but only if they allowed me to bring the dog to work. They agreed to that. No one else could, which I'm sure was problematic for some of my coworkers. As long as I had my dog, I didn't care. I put it out there and it worked, but I also did the 100's of hours of training that allowed me to have a dog that was able to be at a job. Keep in mind, however, most people will say, "no" no matter what. You can be one of the most competent, responsible people in the world with a dog to match, but because you have a dog, most will hold that against you when it comes to work.
Some jobs prefer you have a van/camper and a dog. Working a fireworks stand comes to mind.
Having a pet requires a lot of sacrifice. Are you willing/able to give up your job, your stuff, your current residence, and whatever else to have your pets? Are you willing to make the time to train your dog(s)? If so, you can make it work. It isn't for everyone, but for those who want to make the sacrifices, then it certainly does work. Good luck!