We have "just one" child, who apparently was the model for the book "Your Fussy Baby and High-Needs Child". In retrospect, we feel very lucky that she was born first instead of third or fifth... or eighth.
Today she's 20 years old and a college junior. She routinely teaches her classmates how to cook, how to clean, how to do laundry, how to change the oil in a vehicle, how to unplug a toilet, how to apply for a credit card, how to balance a checking account... you get the idea. She helped me change out a toilet when she was eight years old, and it created some family stories that we still laugh about today. She had her checking account at age 9, her credit card at age 13, her first job at age 14, her first IRA deposit at age 15, her first oil change at age 16.
Each child presents their own challenges in their own ways. Instead of comparing your kids to someone else's kids, perhaps you could compare your current life (and relationship with your kids) to the life (and relationship) you want to have. It's hard now, and you're unhappy. The suggestions you're getting here may seem overwhelmingly impossible, and I'm sensing some "Yeah, but..." in your responses. If you make one small change every week, that'll give you time to see how it affects the kids (and you) and to decide what you want to do next. That will at least start you on the road to "less unhappy".
Or you could continue picking at the suggestions until you find the perfect solution. Good luck with that.
Kids making own lunches: Great idea, maybe I'm just chicken. Our standard school lunch is a peanut butter or sunflower seed butter sandwich, apple slices (I know whole apples would be quicker but they really eat them up if they're sliced and tend to waste a lot if they're whole), hopefully a vegetable of some sort and "treat yogurt" (Yoplait greek, <10 grams sugar and >10 grams protein) when it's been on sale and I've had coupons (won't buy it otherwise). They have no way to heat up leftovers at school, and I really don't want to ask them to eat cold dinner leftovers. Issues: One son is allergic to peanuts, and the other won't eat sunflower seed butter. If he makes his PB sandwich I'm afraid he'll get PB where the allergic one will touch it. Maybe I just need to supervise him closely for a while and make sure he knows how to do it safely, and have them make their sandwiches in separate areas. I still fear giving them sharp knives...should I get over it? Are 7 and 5 year olds old enough to cut up their own apples and veggies?
Yes. You are chicken.
The point here is to train your kids to tackle their own chores. They will not do it as well as you can do it. They will not measure up to your standards. That's not the point. The point is to teach them to tackle their own chores in a safe manner (you're also keeping an eye on their safety while they're doing it) and to help them develop their own standards.
The answer to your "Are they old enough" question is generally "Yes. The oldest is old enough, and probably the middle one too." They're old enough to cut up their own apples & veggies because you're teaching them how to do it safely and then (this is the important part) keeping an eye on them while you're doing it all together. That means three knives and three cutting boards, and eventually four. Ideally with separate food prep stations you won't have peanut contamination, but you know how to handle that better than I do.
I'm not sure I understand why do you care what temperature their dinner leftovers are. More to the point, which is more important to you: having more free time to spend with your family, or ensuring that your kids have a hot lunch? They can put together the next day's lunch right after dinner, keep it chilled safely in the fridge overnight, and take it to school in a paper bag or a thermos pack. It'll be fine by the time they open it up.
Laundry: How do economies of scale work in with that? I do think at least my 7yo would be capable of doing laundry, and would probably get a kick out of it, but he doesn't own enough clothes to make a full load and I really don't like running the machine to do small loads. So I combine everyone's laundry and sort by color, only doing a load when there's a full load of darks, lights, whites, towels/rags, or diapers. Did your daughter have enough clothes to get a whole load without running out of things to wear?
Our daughter bought clothes at Goodwill & garage sales, so she had plenty of clothes to wear while generating a full load of laundry. The kids could also add their bed linens or bath towel to that load, especially if they want to combine loads.
This is not about optimizing laundry loads. This is about teaching your kids to do laundry. There's going to be some inefficiency, some waste, and some downright messes. It's training, not perfection. However it's great family time together, you're getting a chore started on their time instead of just your time, and you're teaching them life skills. So perhaps the "economy of scale" is the least of these priorities. Set your expectations low and don't try to teach everything on the first load. Try to find something positive to say about each attempt instead of going straight to the deficiencies. As your kids do more laundry loads, they'll get better about sorting and full loads and all the other advanced laundry techniques.
Kids helping with dinner: I love this idea, I really do. In our current stage of life, my toddler is pretty high maintenance in the late afternoon, so cooking dinner is challenging enough let alone trying to let people "help" me at the same time. On a good day, I will do the dinner prep while my 1yo is napping...but this precludes having the other guys help because they are at school at that time. Maybe in a couple of years I'll be able to do better than this.
Crockpot: I love how people think the crockpot is the best thing since sliced bread. I do use it sometimes, but I find that whether you throw stuff in a pot in the morning or in the late afternoon, you still have to throw stuff in a pot. And oftentimes, some of that stuff still has to be cleaned and cut up to some extent. Throwing stuff in a pot in the morning while also trying to get everyone out the door is at times just one more thing than I can juggle.
You may be able to find something in your dinner prep that can be done ahead of time when the kids are home-- especially the evening before. Washing ingredients or mixing the dry ingredients? Cutting veggies? Cooking something after dinner for the next day and then leaving it in the fridge overnight? Give them a chore during dinner prep-- even if it's just fetching utensils or setting the table or stacking dirty dishes in the sink or wiping counters. Load up the crockpot the night before, stick it in the fridge overnight, and just plug it in the next morning.
You could take this question straight to the Dollar Stretcher Forums (stretcher.com) where people with a lot more experience than me have made this work for years.
Cleaning the floor less often: Haha, I feel like I already do that! And I hate it! The feeling of crumbs and dirt under my feet is like nails on a chalkboard, so I get very twitchy if I go many days without sweeping. Mopping is a different story...I barely ever mop, even though I really wish I did. Vacuuming...Our den has a dark green carpet and if I don't get to it once a week, I'm very unhappy.
OK, perhaps you're not willing to choose between family time and clean floors. In that case, how about family time by cleaning the floors? Kids can vacuum, sweep, and use a foxtail/dustpan.
Here's a general guideline to consider: if nobody does things in the house as good as you can do them, then everybody will continue to "let" you do them. Training is all about achieving a minimum standard with a minimum level of safety, and then improving from there. If you expect them to ramp up to your personal standards on the first attempt, then you're going to end up doing it by yourself again.