I generally delay a bit in responding here, as I'm not a parent, and I suspect you'd prefer to hear from parents who have experience with Aspies. My experience is as a Sunday School teacher, 7th and 8th grade. Like yours, the kid I'm thinking of was initially diagnosed as having ADD, and later as having Asperger's. He is a bit unusual for Asperger's, in that he's an extrovert. He's also a really nice guy. But in 8th grade he was kind of a handful. I had a high school student helping me. He ended up dealing with this kid when he needed one on one attention. He got treatment, and by the end of high school was no longer noticeably unusual.
I found that when talking with him I had to be really specific. The worst thing you could do is say to him was "stop it." He normally won't know what you mean. He'd know you're upset at him, but not why, and get confused. When something he did caused a problem, I'd say "you're doing
The other kids react this way
. here's why
Please do
instead." And he would. That is, both instructions and discipline needed to be really explicit. In fact now and then he was just being a teenager. But even if I thought he behavior was due more to being a kid than Asperger's I'd still bury him in psychological explanations, as a safer form of saying "please cut it out".
He also tended to react badly to unexpected things. One time he discovered on arrival that the choir was singing that day, and he hadn't been expecting it. He kind of panicked for a minute. The parent of a different younger kid with Asperger's had a similar observation. He said he was very careful about preparing his kid in advance for anything new. They would visit the school before Sept, etc.
The only problem I had with my 8th grader in terms of content was metaphor. I couldn't get him to believe that when Jesus talked about cutting your hand off, he wasn't serious. I don't think he was putting me on. (Ironically, he's now in college, and wants to be a high school English teacher. If he's figured out about metaphors, he'll be a great teacher.)
The most serious incident I had with him is a pretty good illustration. He came back from a visit to Texas with a Texas accent. I'm pretty sure this was not just unconscious, but that he thought the accent was kind of cool. He participated in class as normal (he tended to talk a lot), but in character, as it were. One of the other kids thought he was making fun of the class. He wasn't. He didn't understand that when people behave unusually, others often read motivations into it that may not be their real motivations. Of course the other kid said "stop it" at increasingly high volumes. Not the way to deal with an Aspie. They just about came to blows. I had to take him aside after class and explain why someone reacted that way to his accent.
It's pretty common for Asperger's to go from parent to child. Of the two kids I've referred to here, both fathers were tested at the same time their kids were diagnosed, and they also had it.