DS2(13) is a real stirrer. Loves to wind his siblings up, usually DS3(11), who just takes the bait and goes for it, descending into an all out brawl more often than not.
Banishing them to their rooms has always worked well. However, I reckon it won't be long until DS2 towers over me. Removing privileges, which we always do, isn't immediate enough as they always need to be separated as it just continues otherwise.
So, those of you well into the teen years - can you still send them to their rooms? Or will you simply be laughed at?
I tend to say "I suggest you chill out in your room until you've calmed down", and then walk away myself. That way, there's no confrontation left as an option - I've gone, so no-one to argue with IYSWIM, so he takes himself off anyway, but it's not an 'order' that he can argue against as he loves to have the last word.
Realise this is different from separating two teens.
When he was 13yo, and as tall as me I told him to go to his room. He looked me in the eye and said "No!" I picked him up, and placed him in his room, saying "I am your mother, and when I tell you to go to your room, you go to your room."
Whilst sending them to their rooms works at the moment; that may not last forever. As part of asserting themselves; they may eventually find ways to steer round this. There is also the fact that if it happens often; you may have DS2 (in particular) spending too much time alone (which sounds lovely as a parent if she is a 'real stirrer') but can have a negative impact if she is also experiencing the full whack of puberty. I don't know if there are times when the girls seem to fight more than others and whether something can be put in them to make sure that they are doing different activities away from each other more often. Also maybe rewards for resisting fighting can be offered.
Don't worry about DSs reactions. You are the boss and that is not up for negotiation. You are entitled to deal with their behaviour as you see fit.
As kids grow they need more grown up punishments. With mine it is a case of getting as close to the natural consequences of bad behaviour as possible e.g. they fight for half an hour; they give me half an hour of housework back (making better use of their bodies), they break something; they repair it etc etc. This takes energy to put in place when all you want to do is shout at them - and I have to get some time to think clearly. But behaviour improves if they know that they will have to pick up the flack themselves. Good Luck