My house is always immaculate. On a Wednesday, in fact two Wednesdays per month to be precise. That is when the cleaner comes! 
Luckily my husband is not obsessed with a clean house. He is concerned with happy well adjusted kids and to have a happy home environment for us all to thrive in.
His issue with a sweet wrapper on the floor, would not be in terms of my tidiness, but a child big enough to eat a wrapped sweet should be old enough to take their rubbish to the bin!
I must admit though, it is a lot easier to keep the house tidy with a 10 and a 7 year old, than with toddlers. They can entertain themselves while I get on with things. A toddler cant.
How much time does your husband spend being a dad? How often does he get quality one on one time with his kids? And you? How often does he do bed time with them? Read them stories and chat to them?
My husband does this almost every evening. It is a fair division, I get the morning and the morning chores, and he the evening ones. This suits us. He needs to get to work, I have flexible hours. I am lucky in that I can wrap my working hours around the kids school.
How often does your husband take them to the pool, cinema, activities?
Mine does on a regular basis. He goes off with them on a Saturday or Sunday at least once a month, letting me potter or do "my own" thing. He takes them cycling, skate boarding, swimming, or to event such as Farnboro airshow, etc.
He wants to do these things. He enjoys his children and time with them. He likes spending time with them. He also likes that I am happy. That I get some time to do gardening, meet up with friends, or what ever. Some weekends he go on cycling events on his own, so it is only fair that I also get to just do my own stuff. Most weekends we spend together though.
From the little you post I gather you live in a 1960's Swedish Bergmanesque novel. (Fanny & Alexander for example). The Man in the house reigns supreme, by no other notion that he is male. Separated from both his wife and children, through choice. Because he works, he provides, so he enjoys this unique position.
For an outsider it becomes quite clear that he is both weak and pathetic, claims to superiority, simple from this one statement "I work". Purely defined by this one quality, that he shares with most of the population. Not that he is unique, in any way, or a good father, a good husband, or even a good man. A man who scores points in this way rarely is.
Op, I feel for you. I think you have got a rotten bargain in your marriage, in your choice of life partner.