My mum went thrpugh a period of being disabled when I was a similar age to your youngest, it ended up being temporary although we didnt know that at the time.
I will say that as a 13 year old it was overwhelming going from doing the odd chores each day to cooking, cleaning doing all the laundry etc overnight (although your 16 year old should have more awareness of all of this)
What got to me was not having to do the stuff, but the mental load that I was suddenly expected to take on. Its one thing for a child to do their own washing, or put a load on when asked, its another to suddenly find yourself responsible for all the washing, being yelled at if its not done in a certain perfect way (pegs in the wrong place when hung out, airing not moved around in some secret order that only exists in my mothers brain that I still havent cracked)
And I didnt know how to cook much so I would get an entire meals instructions recited at me and be expected to memorise them. Im a visual person so I need to write them down and I would be berated for being stupid because everyone knows how long to boil potatoes for, unless of course they dont.
Now I am sure you are a lot nicer than my mother, in her case illness just exacerbated issues that were already there. But try to make sure its not always yelling all the time, because thats literally most of what I remember from 13-18 when I left. As an adult I find it easy to help my mum, because I have managed my own home and I can see what needs to be done. As a child it takes awhile to make the switch to thinking of these things, plus you dont have the same leeway for making mistakes as you do as a young adult when you leave home. When you first live by yourself if you run out out of clothes because you forgot to do the washing you wear dirty ones no big deal. If you are 12 and you forget to do the washing you get yelled at or your pocket money docked etc. You dont get the chance to ease into things and pick them up gradually and make mistakes etc
So please take time to explain how the routine works to your daughters, even if it seems obvious to you, even if you think they should know how to do things from watching you. No amount of 'everyone knows how to do that' or 'nobody had to teach me' made me feel any happier to volunteer to help
If they do things but not to your standard, dont tell them off. No one volunteers to help with chores if they think they will never get it right. Gently encourage them and they are much more likely to help more.
Give them structure, routines, charts, all the details. Write down how to make your favorite meals and include all the tiny steps, so they dont feel so helpless.
Dont forget this is a big adjustment for them too. There is a big difference between helping with chores and essentially being responsible for them. As much as you need them to get up to speed right now you all need to live with imperfection for a bit whilst they catch up.
That said absolutely sanction bad language, breaking doors etc, but dont forget they need extra love at the moment. And praise them
My mum used to tell everyone who would listen that we never helped her (she could still get out and about a bit). She would stand there in front of us moaning about how shit we were and how lazy we were knowing full well when we got home we would be cooking dinner, always a proper meat potato and veg meal etc, washing up, putting washing on, cleaning, doing the ironing and trying to fit our homework in. She would say we never did anything without asking but we never got chance because she was too busy barking orders out.
Like I say I am sure you arent like this and this isnt about me, but please give them a chance to adjust and give the all the tools they need to do so even if it is a lot on top of what you are already dealing with