@Redcar87 , OP, I would love to provide whatever support I could offer - any advice or just patting shoulders and giving a hug. You sound like a lovely mum who is taking on too much (on your own).
Like some have said (I didn't read all the posts), your partner is part of the problem. Are you sure you aren't better off without him? Or it's just a sense of fear of change? He's not helping much in any sense, despite you constantly say "He's trying.". What you described is a pure selfish a**hole. Don't you think a marriage requires mutual respect? Does he really respect you for what you bring into the family, or just making up excuses to avoid honour you what you deserve? Relationship is a hard thing for most of the people. But I do think you deserve a better person.
You do sound like having ADHD (I have it). Try to get diagnosed and see if medication can help. If you really have it and it hinders your life, it needs to get sorted. Since it takes time to wait for diagnosis/treatment, better start earlier than later.
And it might help your DSs too. Since it's a genetic thing, if you do have it, there's a good chance the children could inherit it too. (My DS1 is very likely having it.) If they do need support, they stand better chance to get the right one earlier on. But start from finding out if you have it first.
About parenting, I wish I could provide some advice. But each family has their particular circumstance. What works in mine may not work with yours. But one golden principle I believe applies to all is that parenting is about building a long term habit. That means, if you let them watch lots of tv, they get used to it then they would resist doing anything slower paced than tv entertainment. Things like craft or going out for a walk would appears boring and lack of immediate rewards, IYSWIM. Thinking in that way, a lot of things are easy to give in at that one moment. You think it doesn't matter just go easy from time to time. But the trap is that children learn and they persist. So before you realise, they would have lots of habits built up from those moments of giving in.
You don't like them being sad/upset. But the outside world is less compassionate. They would be easier to feel happiness if you teach them to adapt to the big world outside, which means life can't be pivoted around them. That's why it's important to teach them what's right and what's wrong at the earlier age.
But I completely understand your tiredness and frustration and all. It's easier for me to preach parenting theory when I don't have the difficulties of your life.
One of my friends is taking parenting classes provided by the council. I'm not sure if all councils have it and how it's provided and who's qualified or if it's suitable for you or not. But I think you might need some specific advice tailored to your situation. Two under 3s is hard, especially when you work full-time.
Bless you, OP. I feel for you deeply and wish you find a solution to making things better for your DSs and most importantly for yourself.