Hi OP, I have a 4 year old and 1 year old and feel your pain. If they are needy or in a grumpy mood it is relentless. I won't hammer home about your OH but I agree with the other posters. Some things that things that might help you;
I assume you do the food shopping? Just stop buying chocolate and sweets for them. Instead offer them healthier sweet snacks - cheerios, yoghurt and fruit.
Offer picky meals. Try things like oatcakes with peanut butter with berries and grapes, cheddar, rice cakes, slices of apple, orange segments and once they start to eat this then start to add in other more difficult foods slowly. It could start with a small chunk of cheese on the place or a slice of cucumber or red peper, some cooked chicken etc. They might not eat it but it will become normal to see that on their plate at home and eventually (one day whenever that might be) they will pick it up and put it in their mouth. Slowly and small wins with food race.
Try to teach them about a time schedule ie we will play with playdoh/drawing/kinetic sand and then I will have a cup of tea and during that time you can read books or play quietly and THEN once I've had my cup of tea we will go for a bike ride/park/play in garden. It will eventually work if you are consistent. Sometimes I like to ask them to repeat back to me the plan and if they keep bothering me will say things like "When did I say we would do xyz? Have I finished my tea yet?" Etc
Sounds like you're in a bit of a cycle in that they are craving attention and you are struggling to give them attention (because you are exhausted). Maybe think of things you want to do or that you don't mind doing? Sometimes the simple things are the best. I like to take my kids for a walk in the park. I find an area with trees and get them to collect sticks to "build a fire" and I stand there and my input is "oh that's a brilliant stick for the fire!" "Oh this fire is going to be amazing, you're doing such a good job!" And it can take up the whole morning without much input.
Another thing is my kids sometimes play better when I ignore them when I'm cleaning. Can you just be very busy and if they ask for input just say "no, I'm busy cleaning, you can help if you want?" And when they say no just say "well go and I play, I can't play I have to clean" and just say that on repeat until they get the message?
Lastly, look up Dr.Siggie on Instagram. She has helped me loads with my parenting skills. Without being harsh it sounds like you're all just moaning at eachother and unfortunately you are the adult and need to teach them how to respond to things that feel annoying or uncomfortable.