here are some positive ideas that might help a bit - I have notes of other ideas somewhere, but these are the ones that seemed to stick in my mind.
model the behaviour you want. If you want calm helpful people who respect each other, then you have to be calm helpulf and respectful
don't set them against each other (not who can do shoes faster than brother) but can you all help each other to get ready before the timer.
use things like timers. Simply setting a timer has revolutionised my mornings for instance. The timer goes off and we all (including me - modelling the behaviour I want) go put our shoes on. ITs a timer FFS but it works.
use now and next language - and visual prompts if needed. Now we are loading the dishawaher and next we are watching TV. If you need a chart up showing the order stuff gets done in then make one.
don't take stuff away for getting things wrong, give stuff for getting it right - so we can all have half hour tablet time when x is done.
you don't have to join in every arguament you are invited to - just say you will listen when they aren't whining or bickering
if you want to be heard then don't yell from another room whilst doing something else. If its important stop what you are doing and go to them and get eye contact.
Reward charts work with some children. One of mine got anxious so we just literally wrote down everything a child did that was positive during a week. I wrote it on a little slip of paper and put it in a jar (did homework, helped friend, tidied room, said thank you to mrs smith) then on Sunday we ate lunch, lit a candle and read out all the amazing things they had done. We do this regularly. There is no reward linked to it, but they love hearing how nice they are.
I'll see if anything else that could be useful comes to mind.
its never going to be perfect - you have lots of kids and an unsupportive DH. But there are things that can make it better and they are positive things that will help, not more negative stuff.