I think I would make sure your daughter knew it was not okay to be mean to her brother.
Next I would ask your son to draw a picture each time you hear him snapping. Find a clip board to hold the paper, something to fill that other hand and then the pen, pencil, crayons, or markers will fill the other.
Obviously he has some pent up energy that you could use.
My middle boy has had a few twitches himself, hitting his head, snapping, rocking and roaring. I've been quick to redirect these and they fade in a few weeks.
I also have special time with him for half an hour each day while he's doing the homework, and his dad reads with him at night to keep our close relationships with him.
My 8 year old daughter has tics/twitches like this too. I'm soooo lost on what to do. First it was this heavy eye rolling thing, not like a sassy eye roll but where she would roll both eyes to the right and hold it, then stop. That stopped after a few weeks and a grunting starting, which also went away after a few weeks. 5 months ago she had this head shaking/twitching thing...a quick nod to either side (not always the same one) and it repeats...sometimes she does it continuously other times it is random. It went on for a few weeks and then stopped, randomly. It came back last week and is worse. There is no definite time as to when it happens - happy, sad, angry, social, watching tv, reading, playing, etc....it happens during all events. We have had her tested for everything from adhd to learning disabilities to social issues and nothing is wrong with her...she is very intelligent, not adhd, socially fine. She is an only child living with her father and I, mom is in and out and has 2 other children who she has met once, she is very social and does 'ok' in school and she is not on any medications. Anyone have suggestions as to how to get rid of them??? We tried ignoring them, addressing them, threatening to see a doctor who would do lord only knows what (such as a neurologist)...even tried bribing her with "if you stop it, you can have _____." Nothing is working, she says she does not know why she does it but she did admit to just doing it to flip her hair once and it doesn't stop now. Help!!! She looks like she is having seizures when she does it.