Your 10 yr old sounds very,very familiar
I do all sorts of things with my three (4,6,10),it depends on time of day and what kind of mood everyone is in.
I listen everyone’s side and play Judge Judy (state the facts basically and assert who was in the wrong and instruct person to make amends).
I saythat I don’t want to hear it,it’s been a long day,we need food/time at the park and get everyone on a different track.
I reflect feelings,make suggestions for how things could be handled next time. Redirect to something else. If that doesn’t work,announce people are bored and lets put on music and do chores for 15 minutes and then they can try xyz again.
I yell at everyone and escape to my room.
I come back out,apologize and do one of the other things.
So much parenting for my kids involves me talking an it makes me tired. I remind myself my brother and I like each other now a lot.
Also,I keep dark chocolate in my fridge and call mom friends.
(Siblings without rivalry really is worth a read or reread)