What always helped when our lives seemed to get out of control is to step back and take a look at the bigger picture.
Your little one is just expressing her frustration that she wants to be able to do more than she can. the 6 year old doesn't listen because your busy with the baby and the older one and he can get away with it. the 9 year old is .... just 9 lol. a previous poster said this too shall pass. and it will but there may be some things you can do to fix it.
take a good look at the daily schedule is it working? maybe start a new routine. earlier bedtime and earlier wake up time. pack bags the night before pick out outfits and lay them out and have the breakfast dishes out and on the counter along with the cereal and juice already in glasses in the fridge. pack the lunches and have them ready.. empty the dishwasher. (this is a biggie to help morning time) and have a snack ready for the next afternoon.
get up in the morning, dressed all the way down to shoes before breakfast, eat and put dishes into dishwasher, lunches into backpacks. out the door you go.
home from school straight up to the table for snack (unless they do this at daycare) and homework. when done they get a playtime while you fix dinner.
dinner, bath, story/reading time and then into bed with them by no later than 8pm. this gives you time to relax and unwind. 9 year old can read for a bit if he is not ready for bed but mine always were) I always throw a load of clothes into the washer and set the timer to not start for 8 hours. that way it starts in the middle of the night and is ready for me to move to the dryer in the morning.
skip the playdates etc during the week. and if you have had a hectic week you don't need to go do a thing on the weekend. stay home and just unwind. if your kids do not have chores yet give them some. they are old enough. at 6 and 9 my kids each had a list of chores. it helped keep the common living spaces cleared up. they are part of the mess lol let them help.
make an action / consequence sheet and post it on the fridge. teachers have these so your kids will already be aware of them.
action fighting with brother = consequence No tv
action refusal to do homework = consequence no playtime with friend
action refusal to pick up toys at bedtime = consequence toys go into box till weekend.
action 2 year old screaming / tantrun = consequence being put into her room with door closed or time out
trust me they will get it lol. and pretty quickly
hugs to you. and don't worry it does get easier. not less hectic but easier.