The battle doesn't bother them, mama. It only bothers you. They have absolutely NO incentive to help or do what you want. I'm sorry, sweetie, but this is your own doing. You feel that they just need to obey, but that's not how the human race works. There have to be consequences for disobeying and incentives for obeying. Our entire society is based on this. Without it, chaos reins.
You have TOO MANY clothes for your boys. I know it just from reading what you say here. Boys do not care if they match. You don't buy clothes for boys unless they match everything. You have one week's worth of clothes in their closets and drawers. Pants and shirts that match no matter what. All primary colors works well. All the underwear is alike. All the socks are alike. You don't even have to match the socks if you buy a great big bag of them. You keep the jackets in the car.
The less you have in their rooms, the less there is to clean up. They don't get TV AT ALL if their rooms aren't picked up. Any fun game of any sort, whether it's computer or x-box or gameboy just is not given unless their room passes inspection. You sit in the room with them and give 2-step directions. Don't say "clean up your room". Say "pick up the books and put them on the shelves". When that is done "Pick up the trains and put them in the bin for the trains." Etc, etc, etc. You don't leave the room until you are satisfied. If they say no, then there are no privileges. They stay in their room and play and make it even messier, and then find that they have to clean up even more to get their privileges. This teaches them cause and effect and consequences, mom.
To get to this point, go in their room while they are in school and clean it OUT. Bare down to the point where they don't have much in it. Have boxes of toys elsewhere and bring a new box out every week so there is something different to play with. The same for their clothes. And don't buy them much as they grow out of stuff. If they don't care to take care of their things, you don't need to buy much for them.
If they won't get dressed in the morning on time, you start doing the baths at night and put their clean school clothes on them to sleep in. I mean it, too. They may not like it, but tell them when they are in the car by 7:20 for 5 days in a row, they may wear their pj's again. And if they aren't ready to go, they lose their pj's for another week. THIS will work. Take the pj's out of their room until they do it.
If they decide to punish you for this and are so late eating breakfast that you are STILL leaving late, you tell them that they cannot have breakfast unless they are in the car. All they get for breakfast, strapped into the backseat is something boring and fast. If you have to buy whole wheat Eggo waffles and serve them barely warm from the toaster and give them sippy cups full of room temp water, DO IT. They will get tired of breakfast in the back seat and they will hop out of the bed when YOU come in and say "Get up". Let them cry in the back seat, and IGNORE them. Push them out of the car at school and say to them "You know what you need to do in the morning. Do it or this is what happens."
At 6 years old, they need you in their bedroom supervising, not expecting them to adhere to an alarm clock. I didn't even expect my middle school sons to get up without me making sure they were up and in the bathroom.
Treat your 9 year old like the 6 year olds and tell her that if she wants to be treated like a 9 year old, then she has to act like one. Otherwise she will be treated like a 6 year old.
Pare down their stuff. Pare it WAY down. It's the only way they will take you seriously.