I have the same problem re micro-managing. My DH says I should just let them be and they will sort it out but I can't stand the noise and the niggling! I grew up as an only child till I was 13 so I genuinely have no experience of siblings being siblings. DH on the other hand was the eldest of 3 and says everything our kids do and say is normal.

I try to let it go as much as I possibly can but usually, like you, I end up separating them. If it is just words and not nasty words I will try and let them sort it out, once it becomes physical thats when I step in. Also if they are outside and really really arguing loudly then I will pull them all inside because I am conscious of our neighbour.