Would they watch a film with you? You might get an hour respite by pretending to watch a film with them. It will give them some contact (snuggle up) and you might be able to doze on and off a bit.
I used to make a blanket den. Games that seemed boring on the outside take on a magical quality inside a den and might keep them interested for longer. (Add torches maybe)
Another random thing that used to create a lengthy bit of fun was bringing a mattress downstairs and putting it in the living room. They can jump, do forward rolls, play etc. Just the novelty of it makes it interesting. And if they ask for it again, you can say "only when all the toys are sorted and tidied away. When the living room is completely tidy then you can have the mattress for gymnastics".
Also ask neighbours to keep large cardboard boxes for you, the bigger the better. They can create hours of fun. (Boat/ house/shop/ castle). Cutting a hole in one side and giving them 'ice creams' to sell to each other through the 'hatch'. Ice creams, in our case, were wooden building block cubes balanced in the end of empty toilet roll tubes. Red cubes were strawberry, green was mint, yellow was vanilla and blue can't remember.
In terms of immediate options for a rest or at least a break to do your cooking, could you maybe find a local teenager who likes little kids and have them 'babysit' in your house while you are at home? Eg Saturday morning for 3 hours? We used to have a neighbours daughter come in and play with ours - they loved her and whatever she played with them. She had no real responsibility as we were right there but she kept them occupied and earned a bit of money.
Don't worry about a healthy diet for a bit, it sounds like you don't have the spare energy to worry about that right now. You clearly want your kids to eat properly so I'm sure it's something you'll work out when you've got some energy back. For now if it's plain pasta so be it.
Will they eat vitamin/ mineral tablets? Or could you whizz one up in a smoothie or milkshake? That might make you worry less about things for now until you can get their diet sorted.
I hope you are not doing any ironing and only washing undies/ socks and things that are actually dirty for the kids? They don't need their school uniform washed every day.
Can you go to bed when the kids go to bed to catch up on a bit of sleep?
How many days holiday do you get a year? Could you take a day every fortnight during school term time and just rest and relax when they go to school. If husband complains tell him you've got no choice, you need to recharge your batteries.
The ages your children are at now is definitely one of the hardest times. Your 3.5 year old will be developing a mind of their own which often makes the older child struggle as they were the boss until then. But as your younger one develops the skills to negotiate and interact more positively with the 5 year old, things will get better.
I hope you get some answers that help you, even if just a little bit. And once you've had a much needed rest you'll be better placed to think about other issues.
Good luck