Hibiscrubbed has got straight to what I feel is the main point. What he DOES do (the behaviours you listed in the OP) are deeply annoying, but what he DOESN'T do is what I would be concentrating on.
"He doesn’t work much as circumstance’s changed. I may push for him to do more. Financially it would make more sense for me to work more as I can work more but until he is better at domestic stuff that feels impossible."
I found myself nodding along to TheYearOfSmallThings - "It sounds to me as if nothing has ever been expected or demanded of your husband?" He works two days, which gives him three free days for 'domestic stuff'. But instead, "We have a cleaner because he can’t seem to do it." Just how bad was he? And what does he do with all this free time?
"Huffs and puffs and sighs and moans about how busy he is to anyone who will listen. We have one DC age 12, three bed house, he works two days a week. He’s one of the least busy people I know."
Have you ever pointed this out to him, or, given how offended he gets, have you not? Because if not, we're back to "nothing has ever been expected or demanded" of him. He's just permitted to push this narrative of himself which is wholly untrue.
Before you married, what were his living circumstances? Did he live alone, with his parents, with flatmates? How did he manage the domestic stuff then? Was it all done for him, or did he live in squalor, or did he manage? Since you married, has he always been like this or has he got worse? I'm not asking you to post the answers to my huge number of questions
, but I do think you should answer them TO YOURSELF. I think they'll help you to see where you are and how you got here. Because 'here' is not a good place at all.
Armed with those answers, I'd then follow Serendipitoushedgehog's advice -
"Can you sit down with him and tell him that you are finding the marriage difficult and here’s all the reasons why? Surely as the breadwinner you hold the cards in this scenario."
Because I think you have to make it plain to your husband that he needs to start making some changes. At the very least, he needs to acknowledge that he has it very cushy, he's not 'busy' in the slightest, and he needs to pull his own weight at least, in order to model good adult behaviour to your son. Which is why you're on MN asking for help. Because right now, your husband's behaviour is training your son to be exactly like his dad. Your son sees absolutely no downside to his dad's behaviour, because his mum just accommodates whatever his dad does. Drop to two days' work? Mum works. Doesn't do domestic stuff? Mum hires a cleaner. Claims he busy when he's clearly not? Mum doesn't correct him. Between you, you're training him to be like his dad.
I read it here on Mumsnet, and I repeat it endlessly. IF YOU DO WHAT YOU'VE ALWAYS DONE, YOU'LL GET WHAT YOU'VE ALWAYS GOT. So if you want your husband to change his behaviour, then you have to set the ball rolling by changing how you react to it.