I so feel your pain. I'm going through the same thing with my own boy right now. He's on medication and the truth is the medication wears off by the time he gets home from school and he's like a wild man from that point on. I too am at the end of my rope when dealing with his bad behavior and if he does stuff in school like being mean to the teacher and other students well that just pushes my buttons too. I also have anxiety problems.
Here's the deal, when they act out in class and it causes reactions that they feed off of. Like the old boy in the cartoons that liked to poke a stick at the lion. The angrier the lion got the more pleasure he gets. Our boys feed off that anger it energizes them. The more we feel overwhelmed the more supercharged they get. So it's up to us. We have to feel calm, project calm, and feed calm into their minds.
Now my boy doesn't have homework. He gets to read his vocabulary list, read and learn a book but those are extra activities so I don't have any skills to help you there but maybe you can move this to after little sister goes to bed so you're not so distracted and he sees that he has more of your attention.
My baby is also 3 years younger. The two of them are only a month away from being your kids ages. (they have the same birthday) Here's what we do for them. Tiger is the youngest and we start bath, books, and bed at 8 for him. While Tiger is in the tub, G-man is on the computer. Starfall.com, noggin.com, pbs.com he has his own folder of favorites and he's only allowed to go to those sites. It's fun for him and he relaxes doing these things. We then have 30 minutes to devote entirely to Tiger. Reading for 20 minutes before leaving him in bed to watch a video and fall asleep. at 8:30 G-man starts his bath, books and bed. He's reading so we've added learning games to his time, this will also become home work time.
I would suggest taking the ten minutes he's in the tub and get him a snack. look at his homework and see if you have toys that can help. Then you two sit down and play through his homework. If he finishes the next problem, sentence, group of words he gets to play for 5 minutes. (call it taking a fun break) as the weeks progress you can add one more sentence, problem or list before he gets to play. Maybe by Chirstmas next year you'll have played your way through the whole sheet.
Here's the other step.
Don't critcize, ask questions or give commands during play time!!! Believe me it's ooooo soooooo hard but if you say things like
I like the way you.. stacked your blocks
You put... those red blocks together
I'm going to make a stack just like...you did
giggle when he giggle
and do it all with enthusiasm then he will relax even more and so will you.
I'm learning this all in Parent Child Interaction Therapy. G-man's bad behavior has destroyed our relationship and it sounds like you're not too far from feeling the same way.
I'll be here for you if you need to vent. It's better if we vent here rather than screaming anyway. I've been so out of sorts, I know G-man's bad behavior is just feeding off my own.