Under gavelkind or primogeniture inheritance, is a dynasty member who is not a descendant allowed to inherit

You kill your own Duke. So long as the Duke's son (whichever) inherits his father's lands before his mother's there is no way you lose Jazira. The chance of the Duchess dying first is why you are getting the inheritance warnings. If she dies first there's a chance that her heir could end up inheriting Jazira as well when the Duke dies. With Orkney having Gavelkind succession, if she has enough holdings there's a chance both of her sons could be landed vassals of another realm when your Duke dies. If both sons are vassals of another country when the Duke dies, you'll lose Jazira for sure.

As Affine and Studoku point out, the reason your High Crown Authority isn't preventing this is because Jazira is not De Jure part of Byzantium. It only can prevent out-of-realm inheritance in the De Jure Empire. I don't understand why Primogeniture succession in Jazira would be giving the younger son Jazira while the older gets Orkney, that's just backwards. However, so long as the Duke dies before the Duchess, and before either son is landed, I can assure you the inheriting son (whoever that may be) will be your vassal.

I know you have said you don't care to have Orkney, but if you did, the solution would be to kill the Duke, then immediately begin plotting to kill the non-inheriting son. This would assure that Orkney went to the son that just became your Duke.

As you say, this is Crusader Kings. All things are possible through adequate murder.

If for some reason you wanted to achieve your goal without killing anyone (a strange concept, but bear with me): If you have a title to spare (even a barony will do) you can land the son that is the heir to Jazira. By giving him the barony, he becomes your vassal. When he inherits further titles those will also become a part of your realm, even if the titles he inherits from outside the realm are of higher rank than his first title. So long as he is landed in your realm, any lands he inherits become and/or remain a part of your realm.

The biggest thing working in your favour here would be adopting seniority succession, where the oldest dynasty member inherits your titles. With that, you stand a chance of having the King of England being the oldest dynasty member on your death. If that happens, then you take over the KofE as your player character, who also inherits the Kingdom of Ireland (etc), thus uniting the realms in a personal union. (From there, you can take a stab at Emperor of Britannia.) However, this is not guaranteed by any means; unless England adopts Seniority of their own accord, you have to be pretty lucky and/or murder-y to get the KofE to be the oldest dynasty member and then die before he does.

Aside from that, there's no mechanic I know of that's specific to merging realms shared within a dynasty. You're left with all the usual options that apply to non-dynasty realms: marriage/inheritance, vassalization, conquest. (Vassalization in either direction won't work for you since you're both kings.)

There's a couple of advantages you get from sharing a dynasty with your target ream ruler:

• You get a +5 opinion bonus among members of your dynasty, including the King of England. That's not a lot, but it will help you make political maneuvers.

• You'll also get extra dynasty prestige from having a dynasty member sitting on a large & important throne. That translates to some extra prestige for children born into the dynasty. High prestige means higher opinion boosts and better marriage options.

Both of these help, but neither are terribly significant, and both are usually dwarfed by the other factors that are specific to the characters in play at the time.

Conversely, there's two reasons why having a dynasty member as ruler of a target real makes the realm harder to absorb:

• If you're close kin (sharing a grandparent or closer), you run the risk of inbreeding; this makes absorption through marriage riskier.

• Dynasty members are always allies. Declaring war on an ally means that you must pay 50 prestige. If you don't have 50, you can't declare war (probably not a problem for a King).