I wonder if any of your children do this - my DS9 hands do not seem to be connected to his brain. He is often unaware that his hands are picking at, breaking, touching things when he daydreaming about something or talking to someone. It is if they have a control center of it's own. Tonight the raw onions in the salsa I made were particularly strong so I picked them out for him. Whilst he watched me doing this, a second later as he was talking to me, he reached out and grabbed a mouthful to put in his mouth instead of the broccoli. It's so strange!

Our DS doesn't pick or break things as you described. For him, it manifests more as putting things down in odd places or putting on his clothing incorrectly (like his jeans before his undies).

He will do this usually when he's talking to us about some grand idea. Sometimes, we let him follow through and then point out what he did while he was talking and he just busts out laughing. We chalk it up to the "absent-minded professor" syndrome.

Not my own kid, but I see it all the time in my friend's child. He occasionally breaks things he doesn't even realize are in his hands - drives his mother nuts. He's a kid who's always been in constant motion - so much so that he's still falling off chairs at the dinner table, at 10. Kinetic indeed.

Thats DS8. I will tell him to please stop pulling on the stove safety rail and he'll say okay, keep talking and keep pulling. I get louder, he'll shout okay!, take his hands off, resume talking, resume pulling. And so on.
It was worst when he was four and had this sensory need to keep grabbing, yanking, twisting and sucking my hair. I kept training him: a five minute back rub for every minute you don't touch my hair. His hand would creep up within seconds, it was like the Addams family.
I have yelled at him to use his brains to take control of his hands. It does help to remind him of that control.
It's very odd.

DD is always fiddling with something, especially during intense or difficult conversations. I would say that while it's not quite at the level you describe, I know what you mean.

It's not unusual for people to busy their hands and fiddle with things absently. For reasons I don't fully understand, it actually helps focus the mind. Baseball players are an extreme example of exploiting the focusing power of a seeming distraction, which explains why they're engaged in the unsavory habits of spitting tobacco juice, sunflower seed hulls, or gnashing gum like they're chewing cud when they're at the plate.

DD and I both utilize this in nondestructive/nondisgusting ways. An infant/toddler DD who didn't have a toy in her hand was a troublesome DD, so we always kept toys near at hand to offer. Pictures of her in that stage with empty hands are nearly nonexistent. She was usually not playing with the toy, but she had to have it in her hands.

So, I would not treat this as a behavior to be eliminated, but rather a behavior to be modified or channeled in ways that are non-destructive. If I saw him destroying something, I'd call his attention to it, make him clean up any mess he has made, and then suggest an alternative fiddling activity.

I'm with Dude on this one...and I have one who is also in constant motion. Our focus has been
1. You are in control of your body. Your body is not in control of you. You can make choices.
2. This trait is not intrinsically bad, any more than electricity (or natural phenomenon of your choice) is intrinsically bad. It's a valuable part of you. You just need to use it appropriately.
3. Find an acceptable replacement behavior, that channels this energy/sensory-seeking/etc. into something productive.

DD has a friend who has this characteristic. He (as a young adult) usually carries a pocket watch, and sometimes a rock or marble-- anything relatively impervious to his fidgeting with it, and which is quiet to handle unobtrusively.

My son often needs something to fiddle with while he is thinking. At school he ends up doodling or playing with his pencil. The past few years for stocking stuffers her has received a number of different "fiddle" type toys. These are usually well received. I don't see a problem with this but do try and teach him to fiddle "appropriately". We doodle on scratch paper, not books or desks. We don't fiddle with other people things and then loose them or break them.