I know that Ducal war is one of those things that has been frequently requested, frequently rejected. While I am personally in favour of it I can certainly understand though why it has been rejected. It could very easily become a mess and very confusing.
I was thinking however, looting is one of those things that you can do even in an allied realm. That has not caused any chaos or confusion so far, and if something out of the ordinary happens, it doesn't lead to greater conflicts most of the time. But I believe it would be a good compromise between the possibilities for internal strife - actually being able to physically harm your fellow duke and gain from it yourself - to introduce the option for troopleaders to loot in another duchy.
I can imagine it become one of those things that happens every once in a while by perhaps a confused or angry noble that wouldn't cause too much of a fuss. I think it would be very scarce that a duke actually orders to loot his own realm (en masse) but I would /love/ to have that be a possibility. Only the threat of actual destruction to your regions would make inter-ducal strife much more real and on edge.
It would also make people more careful in inter-duchal relations. You can't just piss off other dukes constantly and not expect real retaliation so in a way I think it might even benefit team play on a realmwide level. As well as on a duchy-level where a Duke will have to ensure himself of the loyalty of his nobles to be able to hold them over the heads of other dukes as a threat. All in all, the hierarchy would work like it is designed to. King>Dukes>rest.
I know there's probably not a lot of chance that this will happen, but I felt like I had to try anyway...