Hi, single mum here, two ND kids (11 & 12) and possibly me too. Kids and I home by 4. They do homework, then sort themselves out for school the next day, I float around doing housework and dinner downstairs and helping as needed. Dinner is at 6.30pm. Dishwasher is loaded, we are all in bed by 8.30 (menopause is killing me). House could do with being cleaner but I try and catch up at the weekend.
Things that work for me here ... Not saying they will work for you but maybe something will.
Gousto for five meals. It arrives Monday, I sort all of the ingredients into five separate bags. At least three meals are things that ten minutes to prep and get shoved in the oven for 40 minutes. Pans are at least soaking before we eat or shoved in the dishwasher. When the kids were small and irritating, I set a thirty minute timer, if they hadn't eaten, they were done, no pudding. Eating quickly happened fast and it helped my sanity as I knew there was a limit to the torture. Tvs, screen, background noises were off so they focused. I appreciate the underweight thing but if you can try this for three days, it might help. I will say I'm lucky as the children have mandatory school meals (private school). By when I have done lunches (covid), it was a sandwich, apple, crisps and snack and took me five minutes.
Washing/ dryer has a timer. I put the load in a basket before bed by my bedroom door. I take it down first thing. It's loaded and scheduled to finish so I can take it out and hang it up when I get home. I do one load a day. Colours Monday and Wednesday, darks Tuesday and Thursday, whites Friday. Anything like towels and bedding that wash and tumble dry go on overnight and extras at the weekend. If I have more than one load, I prioritise underwear, socks, pj's and school uniform. Kids have a small washing basket each, I put their dry clothes in there and anything that i find lying around. After homework, they do this. Sorting out their clothes and massively reducing how much they have makes it easier for them to manage this. Ironing is something that gets dropped if we are busy.
Lists! I've been doing this since the children can read, we have a week plan per child listing what they are wearing to school, any after school clubs etc and what they need to pack for school the next day. They manage this. I will verbally run through it to check. We have a list of what clothes they wear to school, when needs packing for swimming, football etc. They have to tell me if they are missing anything before bed. If they are missing stuff in the morning, I will only help if I have the capacity to. This includes fancy hairstyles (girls!).
I use family link, their devices all switch off at 6pm. This gives them a natural window to get things done. Devices stay off until eating and getting ready for bed is done. This includes music. It's amazing how fast things happen in the silence!
It seems a lot of your issues are the dishwashing. Your time is worth more than this. Set a budget, try marketplace, ikea, charity shops and car boot sales and get dishwasher safe stuff or at least stuff that you don't care about. I dishwash everything and if it's still dirty in the morning, I just put it on again to run while I am out. Go for done rather than perfect.
Hope at least one thing helps!