Op, I haven't read all the replies, but I thought I would add my experience as a teacher.
What I've noticed is that all people learn differently. Right now I'm working with adults and it's amazing to see how the guy who can't stop fidgeting and interrupting me (respectfully) while I teach gets a better mark than the quiet student who does all his homework and doesn't move in class.
It took me a while to get used to it, I had a hard time especially with my own ds, who wouldn't sit still for a moment, even for his bedtime story, he was listening while jumping on the bed.
Yet, he learned to read at 4 and speaks 3 languages fluently.
He also has the habit of smiling when he's nervous, which used to make me see red!
Then I thought: what a wonderful gift he has, to be able to keep his cool and keep smiling when something goes wrong. I wish I could do the same.
I don't know you or your son, but when he makes you angry, try to remember that he IS listening and he IS learning. Let him set the pace and follow his lead.
I admire you for the determination to help your son. I might be in minority here, but I agree with you on labels.
When my own ds challenges me, I try to remember that it's a good thing. I'm glad he's not listening. I want him to challenge authority (respectfully) and learn how to argue for his own ideas.
How do you work with your son? Can you find a compromise together with him? Can you find a website to help him improve his reading skills? Would he prefer going to the library and choosing his own books?
Another thought: he could use an exercise ball instead of a chair, which would allow him to move and focus at the same time.
Also, are you doing school work with your ds while your toddler is around? I know sometimes we don't have a choice, but it was impossible for me to focus on ds while keeping dd from destroying everything around her.