I have found that the best thing to do with Duchies is to give them to fellow dynasty members. Let me give some purely anecdotal evidence to support this ('cause I know y'all love stories!).
Now, this may have been sheer luck, but I started a game from the earliest start date as the Duchy of Alexandria. I slowly fought my way up the sibling tree until I was the favored heir (not as easy as it sounds - my brothers were having a lot of wars, and one of them eventually owned the Duchy of Jerusalem and Damietta). I married an Egyptian lady with some pretty great stats. Unbeknownst to me, the patch allows Shi'a to marry Miaphysite. Guess what? Wife was Miaphysite and educating the crap out of my kids.
Yes, this was a lack of forethought on my part. No big deal. I commit to my mistake - my next generation will be Miaphysite. Gosh darn it, this WILL be an interesting and memorable game! And so begins a series of internal wars to make sure that my son's succession will go smoothly, which largely involves removing my brothers from their positions as dukes, and instead installing non-zealous family members with no claims.
When my Sultan finally kicks the bucket, my kingdom was surprisingly stable. I had to give away a king title to avoid a massive civil war with the Arabian territories, since I figured my king would not have time to properly deal with that territory (turned out I was right). But, despite only having Cairo and Damietta as my demense, no dukes flipped out at me.
What I would suggest, OP, is that you take the time (and it can be a bit tedious, but worth it in the long run) to revoke duchies and install your own family as the dukes. To make them even happier, implement elective succession; no matter who gets voted in, they are of your dynasty. HOWEVER, make sure you control the largest duchies personally! While duke of your dynasty will largely be happier than dukes of another dynasty, I find that they can still be antsy during succession. Keep your king's age in mind, and maybe try to stray away from wars in advanced age. Otherwise, opportunistic dukes might very well decide to pounce on a new king during a succession while your troops are off fighting a war.
Now, I don't really know the exact size of your kingdom, but if you really are having this much trouble with dukes warring each other (Despite medium crown authority? How odd!), then you may very well be too weak in relation to them. About how large is your army? How large is the army of this double duke? Even if dukes only have, oh, half of your personal levy strength, I find that the AI thinks they deserve to be Emperor of the Multiverse, which will lead to massive headaches for the player.
tldr: Duchies are good, but you need to know when to give them - early vassal dukedoms can be dangerous!
