Idk man, Kadyrov became Chechen king because his father reached a nice agreement with Russians, basically it was money for loyalty. But Kadyrov's path to his current position was very bloody and in a place where blood feud is a tradition it always means a delayed conflict. Right now he has all power and support, but if for some reason the power in Moscow weakens, other clans can raise their heads once again.
Can't say about Dagestan though, since dunno much about the region, but they always seemed more idk "normal" to me? I have several good dag aquaintances who work and live in a common way, but chechen? None. Anyway, Caucasus has been a hot point for Russia throughout the history, there is no reason why it won't be once again.