Siblings fighting like this isn't easy to witness but is not uncommon. At least they are doing it in front of you and not behind your back, which also happens and then you're faced with who was to blame!
I'm not excusing bad behaviour but neither asked for the company of the other- so they are just fighting for dominance and it isn't always the older who gets it!
Fighting between siblings although not nice, rarely becomes serious, and through it they will establish their own boundaries.
I remember fighting with my older brother until I made him cry- not a pleasant memory. To this day I don't know why I was so angry with him.
As others have said, maybe you are taking on too much, especially as you are becoming anxious and stressed about it.
I would also suggest boredom may be a factor, so diversion tactics work best but it takes some thought and imagination to think of ideas.
I would advise against splitting them up- but give them some space from each other at the same time. However, I would discuss with parents everytime. Maybe they would be better in holiday clubs?
Kids get stressed and anxious too, and also have to find an outlet for that, so maybe trying to talk about it in a calm and accepting way is one option.
Whatever, don't start the blame game- even the best of parents have kids that fight- it's a normal part of growing up.