FFS - you cook AND do the washing up?
Seriously?
How many other women honestly do this?
It matters not a fig that he works and you supposedly do not. I have said this until I am blue in the face, but people get PAID quite a lot of money to do what you do for free. Research how much it would cost in your area to get a cleaner and a nanny. Tot up how much that would be and then hand it to him with the idea that you are going to get a job. So you'll be needing both a cleaner and nanny since both of you will be working. Just see how well that goes down with him.
Looking after kids is no easy life. I am guessing here that you do the weekly shopping? Paying all the household bills? (That's something your nanny wouldn't do) Caring for the kids? Cleaning? Washing? Cooking? Appointments?
For crying out loud, we were NOT born natural mothers/cooks/cleaners. We had to learn and yes we sometimes made mistakes along the way, we've all put coloureds in with whites, we've all burnt the tea and we've all made a right mess of changing nappies. But we learnt. They have the exact same capacity to learn so why why why are you, not just you OP but others who have also said their dh's do FA, why do you allow it?
Of course they are going to come home from work and watch TV, play on the pc and relax after their hard day at work with their proper allocated lunch breaks and numerous coffee breaks. Poor little darlings. Whilst you busy yourselves around them like Mary Poppins.
The bin was a small argument, a trivial one but it's indicative of much bigger problems here and that is mainly that you are acting like a household slave with no respect from your dh, no help and no time off. You wouldn't put up with these working conditions in a proper paid job so why do it now?
Throw your pinny away and do nothing for a while. The kids will survive on sarnies for a day or two. Do absolutely nothing until they agree to help out. And the next time they accuse you of nagging, be less passive aggressive and more aggressive aggressive - perhaps with a frying pan on their thick bonces to jiggle their brain cells around a bit more.