OP please speak to someone about your MH if you ever feel that overwhelmed again where you feel like you need to leave. Look after your self first.
Now - you cannot do this alone - but you need to "go through the trenches" to be able to change anything.
If they have got used to getting their own way, you have to do the opposite. e.g chocolate/sweets - none for bad behaviour. it will feel temporarily "worse" but unless the behaviour changes this will continue their whole lives and make your parenthood journey filled with fire fighting constantly.
If they won't eat - let them eat nothing. you can invole them in the food planning, or prep and/or cooking, and then that is their only option. They will not starve to death - speak to Health Visitor or doctor to confirm.
Wont sleep? Keep putting them back in bed, it will be difficult for a few days but you have to stick to it.
Won't occupy themselves? Sit with them for some tasks but they have to learn to do some things by themselves.
Start with the basics - then you can incorporate the fun. You shouldn't have to cut your working hours down if is not something you want/are able to do.
Your partner should take them out of the house for an activity, to allow you some time to breath and do things you want/need to do as well. Showering, eating, cleaning are NOT wants, and that is the bare minimum someone should be able to do.
If your partner does not pick up some of the load, and or give positive input - you might as well be a single parent and only have your children and yourself to deal with rather than thinking of another adult.
Big hugs to you, this is very difficult alone, hoping you can find the strength.
Take a breath as many of us have felt this way and it really is exhausting x