If you don't think it's malicious, then you need to have a serious chat, and then pull him up on his bullshit each and every time.
You need to sit down with him and tell him you are absolutely furious with his lazyness and you can't tolerate it any more. You are his wife, but not his mother/housekeeper. If it's his job to do the dishes, then he needs to DO THE FUCKING DISHES. He needs to know that you really are at breaking point, and you won't keep turning a blind eye to it.
The next time the washing up gets left until the next day? Walk over to him and tell him "Do the washing up". If he says "In a minute" then say "No. You lost the right to decide when to do things in your own time when you decided to simply never do it, and leave the dishes for days on end. Do it NOW, or get out".
Waking the child? His job to get said child back to sleep. It doesn't matter if it will take him five times longer than it would take you. HE woke the child, so it's HIS responsibility.
Look, at the end of the day your kids are learning that cleaning is women's work, and not something for men. That men can ignore their chores and it's okay because the wife will pick up after them. That's such a bullshit attitude for kids to grow up with.
This might not be something you want to finish the relationship over, but you need him to believe that it could be.
No-one should have to put up with someone as bone idle as this.
If needs be, he can look into counselling to deal with his childhood or whatever.
After he's done the fucking dishes.