It's him. 100 percent. There's no excuse for denigrating a partner and children and acting like they're a burden when they're the result of his own free choices.
The key to this is where you say you tell him that if he doesn't want kids and a family then he can fuck off and live by himself and he ignores you, and you presumably accept his silence. He's learned that he can denigrate you, make exaggerated complaints, act like a victim when he's not... and there are NO ACTUAL CONSEQUENCES.
What you need to do is find your centre, sit down calmly and set some real boundaries. Next time he complains or says he does everything or acts like you and the children are an imposition on him, make a note. Later, when the kids are in bed and you're calm, sit down and tell him something like:
"DH, today you said [insert whatever he said]. For many years I have noticed a pattern of you blaming me and the kids for stopping you from doing what you want to, complaining when the house isn't perfect, exaggerating your contribution to the household chores, ignoring and not appreciating the effort I put into parenting and keeping our home comfortable and generally acting like you don't enjoy the life you have. This is incredibly hurtful to me, it kills the love I feel for you and it makes me not want to continue a relationship where I don't feel loved and appreciated. It also hurts my heart for the kids, to see the disappointment and shame on their faces when their Dad treats them like a burden.
I work hard to make this house clean and comfortable so it feels like a slap in the face when you nitpick something that's not perfect or say you do everything because that's simply not true and it ignores my hard work.
When you blame the kids and I for your poor time management or lack of communication about what you need to get DIY done, I feel frustrated and resentful because these are problems we can't solve for you. And I feel sad and worthless when you agree to spend time with us and then clearly show you're not enjoying our company and would rather be elsewhere.
I don't like living like this. It hurts a lot. And it's hurting the kids. I want to be in a relationship where I feel seen and appreciated, not a chore to put up with or an inadequate partner who is constantly failing to meet your standards. I am who I am and you chose to marry me. The kids are who they are, you chose to have them and you raised them so if you don't like how they behave, you need to think about how you haven't taught them better. And yes, family life can be busy and involve a lot of juggling and frustration but you chose this life, you chose ME as your partner, you chose to have kids, you chose to buy this house with the DIY it involves, you chose it all.
If you now really feel that family life isn't for you, if taking care of the home you own isn't the way you want to spend your life, that's fine. I'm not going to force you to keep living a life you don't like. If you think you'd be happier separating, selling the house, doing 50/50 care, living a different life, you can and should, because right now, this marriage feels goddamn miserable for me too. But if you still want a family, a shared home, a marriage, then the complaining and blaming and acting like a victim has to stop NOW because I'm done putting up with it.
If you don't know how to manage your feelings when you're frustrated and communicate your needs in a respectful way, then I'm happy for you to get counselling, or for us both to go to counselling. But I'm not going to continue a relationship with you if you keep treating me like I'm worthless and our children are burden to you. So, decide. What do you want? Because you can't keep enjoying the upsides – and there are a lot of upsides – of having a wife and family home, and keep behaving like your wife and kids and home are something unpleasant that you have to put up with."
That's what a firm line in the sand looks like. And you have to mean it that you're done putting up with it, too, and be prepared to leave yourself. Because if he knows he can say something like "Oh for god's sake, stop making a big deal out of nothing. Jeez, everything has to be a drama with you. Fine, I'll try to be more cheerful. Happy?" and you will just sigh and keep putting up with his shitty treatment and disrespect, then guess what you're going to get more of? That's right! Shitty treatment and disrespect.
So this isn't really about him making a choice about what he really wants. It's just as much about you making a choice about what YOU really want.