Earlier you said that DH job is" not physically demanding, just mentally. "
A mentally demanding job can actually be more tiring than a physical job.
Physical means the body gets tired, we sleep and are refreshed, but mentally tiring work can lead to disturbed sleep, inability to sleep etc etc.
Im not saying this is the case, just that it could be a part of the problem .
You are making yourself a martyr, of course the kids can help more. Its teaching them life skills and a healthy attitude to taking responsibility for their own things.
You say when he does do stuff its not usually done properly! Maybe he does not reach your standards but he is helping. Maybe your standards are too high, again making a martyr of yourself. Do you do the " oh I'll do it myself" routine?? Hardly going to inspire him to help if anything he does is not good enough. Why would he want to help if anything he does is just going to be negated.
Yes I know its not "helping" and it is actually his responsibility too but if you nag him about how badly he has done it he is gonna back off isnt he.
Allowing your dc to get up at 4am is definitely not helping matters and I would say is a bigger problem with your state of mind than the fact that you have a husband who does not meet your housework criteria.
This is behavioural and has learnt a habit because you have allowed it and given in to it. Only you can undo it.
Stop being a martyr
look at the real reasons you are so unhappy with your lot
Bloody hell I think there would be lots of women on here who would wish they had half of what you have, a husband who works , healthy children, a nice home.
Surely a bit of dust and family mess is not worth getting so stressed about.
Learn to appreciate the good things and stop sweating the small stuff.
When they get home from school and DH is home from work, just say "sod it, lets go out for a picnic, walk, play on the beach... anything thats different from your normal "work routine"
Watch their faces , you may surprise yourself too and enjoy it and I promise you the house will not melt because the kids left their toys out, and the garbage didnt get taken out 