Really helpful biglittlemedium 
Op I think you may be over-thinking this and simply lacking in confidence in your own parenting skills. I wouldn't stress too much about strategies and rules, but your relationship with your DC. Parenting books seem scared to use the word "love" but basically that is what lies at the crux of it all. And proper love of course means giving your children what they need and not necessarily what they want (ie equipping them with the essential skills they need to fulfill their potential and be "successful" adults once they leave home).
So can you reframe how you look at "managing" or "discipling" them in your mind, and think of it instead as "teaching" "guiding" "modelling"?
And you can do it in several ways (i) first and foremost - walking the walk modelling good behaviour (ii) discussing and getting them to come up with solutions to problematic behaviour with you as back up (iii) with humour and making it fun (as much as humanly possible anyway) and when all those strategies have failed (having sorted your parenting priorities clearly in your mind and picked your battles) (iv) following it up with discipline like turning off the wi-fi.
I could be talking through my hat mind you as I only have one child and I am not a hugely experienced parent. And I do doubt myself a lot, so can identify with you second guessing yourself because I do the same. But at the same time I do think children basically want to be loved and feel secure - part of a team - being "led/guided" gently along towards clear objectives and expectations, with fun along the way. All a lot easier to write down than carry out in practice of course.
So to take your example of why should they do homework before watching videos - it's not about you arbitrarily imposing a good habit on them for no reason , it's because you know that it will stand them in good stead for their future life if they can develop inner self-discipline/ self-control etc because that is what so often lies at the heart of living a successful and fulfilling life for them. DC are often impulsive and they don't have the insight to defer instant gratification and don't understand the long term consequences of constantly putting off study/exercise. So it's our job to teach them that. Maybe that is a very old-fashioned view now though!
In summary: you CAN have more of a say than them, because ultimately, they are the beneficiaries.
And of course, things are much, much harder during lockdown, so try not to give yourself such a hard time! Give yourself permission to have a break and do something you enjoy once in a while. It's good for your DC to see you happy and fulfilled and not stressing once in a while.
Finally, fwiw, I think parents who doubt themselves, get anxious and don't think they are doing a good enough job, are often better than those who have supreme confidence in themselves and never question their own strategies!
As for your house-cleaning strategy tomorrow, instead of sending off the DC to sort out their rooms alone while you tackle the rest, which is a bit boring and lonely for them, how about you mix it up a bit, make it a team effort, put on loud music, set a timer, and all pick tasks out of a jar, or cross them off a white board together, give them tasks slightly above their skill levels, which makes the DC feel more responsible and "invested" ifyswim and it's a bit more fun doing it collectively. It may not be up to your standards but they may be more willing to try again next time... .
Disclaimer: all of the above strategies go a bit pear-shaped again when adolescence hits of course 
I find the parenting website "Kids in the house" to be well balanced and helpful.