I actually see Dark Eldar society as relatively stable. Sure, there are the occasional bits of infighting, but you can't just go up and kill whoever you want to, because they're most likely a member of a Kabal, and if you mess with one member of a Kabal, you mess with all of them. You've either got to make sure noone can put the blame on you, or make sure that you wipe out every single one of them. To be fair, Low Commorragh is probably just as unstable as you describe, but once the Kabals start having noticable levels of power and influence, it becomes increasingly hard to simply kill off a member of another Kabal.
The same goes for internal struggles. Each Kabalite needs to balance trying to get ahead with not appearing too power-hungry, because they'll simply get killed off themselves, or most likely sent on a suicide mission/placed out of the way if their betters get wind of what they're planning/potentially planning. I prefer a more Machiavellian interpretation of the Dark Eldar, where there's still lots of backstabbing, it's just that most of the time it's political backstabbing. They aren't the Orks, where full-scale brawls break out because someone looked at someone funny, they're far too "civilised" for that.