OK, I'll be the one to say it. I think there are some psychological issues going on in the individuals and relationship dynamics in this situation that require professional help by a licensed professional. I'm guessing things that are something like learned helplessness, pessimistic thinking, control issues, background of normalized chaos, and such. I'm not professional so I'm not qualified to label or diagnose anything, but the chronic paralysis for doing routine things like childproofing; sending a child to bed when it's late even though he's giving dad a back rub; insisting on not being able to do anything about a child seeing adult content; controlling issues related to sharing the car, buying a stool, threatening to tear down curtain rods; and other things listed aren't going to be solved by sharing ideas from others who have homeschooled through similar situations.
Lion, I hope you find someone who can help you and your family through this difficult time.
I read quickly through this thread. What stood out to me most was the thought, "something's wrong, and I don't think it's the OP's ability to homeschool or the time she finishes school each day"
Right now things are tough. You've got a kid who is old enough that he really should be doing schoolwork. You've also got a toddler who is making that very difficult for you. But worst of all, the stress is causing you and your DH to butt heads with each other.
Gently, because I know you're stressed, and this thread has been pretty harsh, I think you should try to focus on your relationship with your DH. I think you said your DH isn't interested in marital counselling, but that doesn't mean there's nothing the two of you can do. Can you put the kids to bed early, or get a babysitter, and go to a coffee shop (or somewhere without kids) and talk?
I'm no marriage expert, but if I were in your situation (and I have been in a similar one where I realized we needed to work on our relationship, and DH didn't really notice that it was in a not so good place) I would read articles/watch youtube videos about how to fix the relationship, stuff like "how men's minds work" or "how to communicate with your spouse" etc. Someone else probably could give you better suggestions.
Remind yourself why you married your DH. Think about your goals. Then go to him. Bring up those happy memories from the beginning of your relationship. Get him to talk about his goals. Goals for his career, goals for the house/location, goals for the kids. Tell him, without venting at him, what you've been wanting. That you want to communicate with him. That you want to live in a home that works for you, not against you. That you need functional shelves, for example. Tell him that sometimes you just want to be able to do home improvement projects too, and that you need the right tools for your new "hobby". Make analogies to his office, if needed.
I've said to my DH "you wouldn't like it if I came to your workplace and left a bunch of plates all over the desk and printer, poured out your garbage can, and emptied your drawers." I used that to explain that homeschooling is a job for me, and that I don't have time to clean up the mess that 3 other people are leaving all over the place each evening, and homeschool, and keep the kids fed and cared for. He started helping me with the dishes and cooking.