L.C.
It seems like you get involved in the arguments and such. Stay out of it. Tell them to deal or go to their rooms. He is pubescent -- she is a tween. There are hormones raging!
If they start acting up, don't ask who started it, just send them to their rooms for a time out. 15 min. each ought to do it.
I used to make my kids play in one room together without talking for 10 min. They didn't have to play together - they just had to be. More often than not, they'd want to stay together after the 10 min. Sometimes I put them in front of a puzzle at the dining room table, other times I'd put them in a room with a bunch of legos on the floor. They didn't have to work together, they just had to be - and NO talking.
They learned to apologize, get along, and just be.
LBC