I have five kids like you Kitty and kinda the same ages.

I hear ya on the DS2 behaviour. Mine is just truely horrendous some days, BUT I let it be known that, "I am the boss of my household buddy you WILL play by my rules or you will lose!!!"
He has days where he spends alot of it in time out. If he is being destructive put him in the toilet. Take everything out and leave him there. Or strap him into a highchair in the middle of the floor.
You need to be hard on him and consistent. It will get worse before it gets better but you have been through this stage with your other kids so you know you can do it.

Your DH, im sorry but he sounds pretty bloody hopeless so I would give up wasting time trying to get him to help more or to change and just focus on what YOU can change at the moment.

DD's homework, sounds to me like you are taking over a bit there. They are given homework that they can do (with minimal parent help if needed) on their own. Your DD's teachers obviously think she is capable so why are you spending 6-7 hours helping???? If she cant do it then maybe you need to speak to her teachers.

I menu plan and have 6 weeks worth of menus that I rotate so I know in advance what I A) need to buy and B) what I need to take out the night before to prepare.
It did take me a little while to sort it out but I simply made up a list of all the meals we eat then I spread them all out over 6 weeks.
Its not in stone so if I forget or cant be bothered then noodles it is, no biggie.

When the kids are at school it only takes me half and hour to an hour sometimes depending on what we have to prepare the meat and veges and have it all ready to chuck on at 4.30pm. Do you have a slowcooker? It has been my sanity saver on many occasions.
If not the kids will not die if they have eggs, spaghetti, baked beans or soup and toast for a week just while you get on top of everything. No reason why older kids cant help prepare this either.

Its all about organizing yourself and it sounds like you dont time manage very well. Im sure Chakotay does sleep at times and yes in a perfect world (or house) we would have a sleep too but with five kids its not always possible.

The kids arent always home requiring you to be the referee so what are you doing with your time when they are at school and daycare? I understand Chakotay is demanding alot of your attention too but he has to learn as well that he has to occupy himself if Mum is busy.

Sorry if I have come across a bit harsh hun but I am one of those that know how fast things can fall apart if I dont stay on top of it. DH calls me anal sometimes because I have my ways that things have to be done but I know it works so thats the way it will stay

Stop making excuses and start with baby steps. Include the kids, time them and make cleaning up a race and fun. It is not impossible you can do it.