Oh I am sorry your family is going through this. My DS6 sometimes has big tantrums which upset the whole family. It is frustrating and exhausting. I can only imagine at 10 yrs old it would be harder to deal with.
I second the idea of looking into his medication. I remember my little brother being tried on Ritalin and while it helped him at school, at home (when it was wearing off) he was a disaster, behaving completely unlike himself.
The only other advice I might suggest is trying to understand if there is a pattern to the tantrums and seeing if there is a way to avoid the triggers - is he hungry, tired, frustrated, etc.? Once my kids are in the middle of a 'big emotion' (anger, anxiety, whatever) there is not a lot of value in trying to reason with them. I've found the best I can do is comfort and empathize with them and save the rational discussion for after. I also try to help them verbalize their feelings (ie "You look like you are having a big feeling! Are you feeling very angry? You are mad at me for [what I said, did, etc].? It's OK to feel angry, when you are calmer we can discuss [x]")
I have also found some useful tips on this site:
http://thinkkids.org/does-your-child-ever-seem-unreasonable/?It is hard to remember parenting advice when you child is in a tantrum state. But I found the "Regulate, relate, reason" approach a useful one.
