After every argument I pour over the details trying to work out how I can change and be better next time.
Stop. None of this is you. It's all him and it's abusive.
And don't fret about what makes him do it (eg he's emasculated because you're working and he's not) because that doesn't matter. All that matters is that this is how he treats you. You need to survive. You need to thrive. You probably won't be able to do that with him.
if I’m going to stay I need to find a way with being ok with being at fault (in his eyes) all of the time.
It is possible to stop caring about someone, for their words to wash right over you, to make your life robust by not caring about what they say or do.
But it's dangerous.
As soon as he sees you aren't in bits because he's angry, he'll up the aggression. You need to be aware of this because it could put your life at risk.
Have I missed some details along the way? I know you have three children, one with additional needs. I don't know if you are married to this man. I don't know if you are owner-occupiers of your home or if you are renting. I know he does all the childcare - and I know you need legal advice.
I suggest you start therapy as soon as possible. Talk about how it feels to be in the wrong all the time.
Also, instead of trying to adapt to live in the abusive situation he created for you, look for some small place near school, or near your family if you have them, where you can live with your children.
Very best wishes. I hope you find a way to get out safely and set up a much happier life for yourself and your children.