It is utterly absurd that your Crown Authority laws have ZERO affect on your vassals if they are subject to another De Jure kingdom. Oh, it's zero effects except for the relations penalty. Who's bright idea was this?
If you're playing as an independent Kingdom of Bohemia or Sicily, it seems, your Crown Authority NEVER takes effect, because the HRE/Byzantium laws are always superior. This doesn't make any sense. Why should it be that my clever machinations to force my scary neighbor's Crown Authority laws downward result in my own vassals suddenly becoming free? There is nothing I can do to prevent my vassals from fighting one another besides pray that the Empire raises its Crown Authority.
It is really frustrating when you have a vassal running around collecting all of the Duchies in your realm, and there is absolutely nothing you can do about it short of becoming a massive tyrant.
This also leads to silliness such as the Duchy of Apulia being un-inheritable if the Byzantine Empire has High or Max Crown Authority. Even if the inheritor is also located in the De Jure Empire!
At least disable the Realm Laws for Kingdoms that are underneath Empires, so as not to falsely give us the impression that we might actually be able to make the rules in our own kingdoms.