L.C.
You are in a total battle of wills and they think they have you outnumbered. The odds may be in their favor, but time and wisdom are in yours, so take courage.
First you have to find what works. Study them and find what they enjoy and what they hate. Then use it to your advantage. I have one that loves electronics, we take those away. I have one that is super laid back, we make him to chores. I have a social butterfly, we take away social opportunities. I have one who is constant motion, we use time out and early bedtime. I have one we can use any number of these on but usually responds to verbal correction. We use something different with all of them because they are all different.
Every system should be a system of consequences, not rewards. Positive behavior yields positive consequences. Negative behavior yields negative consequences. You are not gifting them for behaving, they are determining their quality of life and day with their actions. Any system you put into place should be consistent. Don't change it just because you don't see immediate rewards.
If you do "A" you get "B", if you don't do "A" you don't get "B" but get "C" instead which should always be something that they both hate and reinforces the need to make the right choices instead of the wrong ones.
Here's an example. If you clean up your toys, you earn 30 minutes free playtime. If you don't, whenyou come home those toys will be gone because what I pick up, I keep.
Structure the day as much as you can. Keep them busy and separate as much as possible. If they can't get along, then playing together should be seen as a reward. If one is playing a video game, the other should be busy playing in his room or outside or doing something completely different. If he complains he can go to his room and lose his game time in the bargain.
Don't give back what you take away too quickly. They need enough time to experience the loss. Don't let them negotiate how long their punishment lasts. Make a statement and stick to it. If it doesn't do the trick, next time make it longer.
Tell them once. Let them know what you need them to do, that they need to do it now, they have a certain ammount of time to do it, and if they don't these will be the consequences and if they do what they are told, then these will be the consequences.
Give them chores. It won't hurt them and furthermore will teach them responsibility and the idea that they contribute to the family out of loyalty, gratitude and community. It will also give them less time to get into trouble. I believe there are chores (like room) that you do because you should and chores (like lawn or laundy) that you can get paid for. If you don't do the ones you should, then you don't get paid for the others.
Give them 20 minutes to change and unwind and then immediately start homework. With my boys, the longer I waited, the harder it was to pull them back in. As to showers, they need to know that at the same time every day they will bathe. If they don't do it, wake them up early the next morning and if you have to bodily put them in the tub and bathe them make them lose sleep to do it.
It's about who's will is stronger, Mama, and you need to decide right now that it's yours because they are only going to get bigger and so will the fights, rebellion, and disrespect. Don't raise your voice, don't get mad, lay down the law, set out your expectations and the corresponding consequences and let them own their choices.