When my son (5) says he doesn't want to pick up his toys and wants me to instead, I say, "I don't want to, either." And then I tell him ALLLLLLLLL the things I do all day that I can remember, like:
Load the dishwasher
wash the counter
clean the table
wash, dry, put away laundry
help pick up toys
cook food
pay bills/manage finances
grow/harvest/plant food
sweep the floor--often three or more times a day
vacuum
(other accomplishments for me, that aren't so much drugery, but are still things that need to be done:
read them books
take them for walks
Make toys for them
take care of the ducks)
All day I am busy. And if I am not busy, it's because I feel awful. So I often describe how awful I feel. Kids don't know--they can't see what you do all day, or how ill you are. I don't think of it as "explaining myself" to my kids, or "defending my activities"--instead, I think of it as teaching them to notice things outside themselves.
When I think back to my childhood, I recall wondering what my mom did all day, other than read books or watch cooking shows....then I realize that the sink/counter/floor was always clean, and she always made dinner. I look at my house and notice a dirty sink, and wonder how hers always stayed so clean....OH, she cleaned it! Same with her stove, and counter, and floor. Kids don't notice unless they are (1) involved, and/or (2) shown.
Maybe have her tag along beside you for an entire day. Show her everything you do. Put a weighted vest and foggy glasses on her for a few minutes, so she can feel how it is to be so tired and weak and dizzy. Show her how hard your life is. You probably won't need to do this more than once to get the point across.
Another thing would be to try to do more things together. Everyone cleaning at once. I notice that with my kids, I can generally start picking up toys and ask them, "Hey, could you put that in the toy box" or "Who can pick up the cars the fastest!" that they are much more motivated to do things. Showing that chores aren't drudgery is helpful, too. Basic home maintance is necessary. It's part of life. Try to enjoy it! Encourage her to put in earbuds of her favorite song while she does things, or make up a game. Help her see how to make the things fun for the younger siblings, so they want to join in. My kids FIGHT over who gets to start the dishwasher (if only they'd fight over more chores, ha!)
Help her to see, also, what her siblings are doing. Explain how they are younger and may not be able to do as much.
Basically, think of her as your disciple. She's older, she's got a more mature brain. Think of how Jesus worked with His disciples: He explained to them what He was doing, while asking them to trust Him. He gave them small responsibilities and then greater ones. He taught them. He rarely got mad at them, but showed His sadness and remorse at their lack of trust or inability to do what He asked.
Of course, that's easier said than done, especially when your tired and just trying to trudge through the day through fatigue and mind fog. On those days, I really have to train myself to STOP, think loving thoughts rather than ugly angry emotions "URG!!! Why can't he just _____?!?!" or "How could he ______!?!? This child!" It's taken a year of training to get myself to mostly respond with love and explanations and teaching rather than fury...and even still, when I'm tired and "just trying to do ONE thing without an interruption!" I still fall victim to the anger. Sometimes, I think, the anger response is higher when one is fatigued because it gives a burst of adrenalin to overcome the debilitating fatigue, even for just a few minutes.
It's hard stuff. Know that you ARE doing a lot. Even if it doesn't show. Even if growth in your kids takes months or years. Even if the counter you just cleaned is dirty again in less than 30 minutes. There was an article I read about stay at home dads, and how hard it is to switch from being able to do a task and having it stay done (I built a shed-check! I earned a paycheck-check! I fixed a sink-check! I logged this section of the forest-check!) to never actually finishing anything. Everything is a work in progress. Every day you have to do the same things over an over, and there's rarely that satisfying feeling of accomplishment and closure.
Ah-ha! I found the article:
https://www.npr.org/sections/health-shots/2018/06/17/619557786/stay-at-home-dads-still-struggle-with-diapers-drool-stigma-and-isolation
Bildner says he finds that men often have trouble breaking out of the work mindset and getting into the world of parenting. At work, he explains, projects tend to be linear — the goal is to finish one task and move forward to the next, then hit the next goal, the next milestone.
But parenting isn't linear, Bildner says. It's more like the ocean.
"The tide comes in, the tide goes out. The house is clean, then it's dirty. Your child is happy, now she's sad. She's tired, now she's rested."
Bildner gestures at the kids scampering around his carpeted basement. "An hour ago, this room was completely clean," he says. "Now it's wrecked."
As a parent, Bildner says, you have to have a different vision of progress. "You just have to accept that things get done and undone all the time. Your job is to just go with that," he says.
Accepting the ebb and flow of a child's world can be hard for a man who expects something he's fixed to stay fixed.