In order to have cadet dynasties, there should be a need to have cadet dynasties. Right now, there is no such need.
If you are King of France (lets say Capet dynasty), and another member of your Dynasty becomes the new King of Denmark, then is in your interests to remain part of the same dynasty. The Dynasty becomes more prestigious, which increases prestige of your descendants, and it also offers you free alliance with each other.
To counteract this, there needs to be a drawback, which is not here at present. Something should compel King of Denmark to change his dynasty. I propose the following:
1) Give more control to Head of Dynasty
Right now, Head of Dynasty is just a figurehead, this needs to change. It should be possible for HoD (in the above case, King of France) to meddle in affairs of King of Denmark in a way beneficial to France, which would compel King of Denmark to break off and form a cadet dynasty. This creates the "need" for cadet dynasties. I propose following measures:
2) HoD approval for dynasty member marriages.
Revamp marriage system a bit -- make it compulsory for every ruler to get approval from head of dynasty before conducting marriages of dynasty members in his/her court (but not himself).
3) Tributes.
Landed dynasty members have to give a small tribute to head of Dynasty in terms of percentage of their income.
4) Mini-excommunication.
Allow HoD power to "excommunicate" dynasty members. I don't mean excommunicate in a Catholic church kind of way, this "excommunication" (I use this for lack of a better word) would just affect opinions of other dynasty members towards the excommunicated member
5) Dispute settlement.
Intra-family feuds are bad. Give HoD powers to settle disputes among non-excommunicated dynasty members.
So, now Head of dynasty has some powers over their dynasty members. This would do 2 things. One, it would make the position of HoD a bit meaningful. Two, it would now give King of Denmark an incentive to break off from the Dynasty.
Forming New Dynasties
So, now King of Denmark has decided he does not want to be part of the Capet dynasty any longer. He will break off. For this you need to keep a minimum Gold and Piety requirement. Once you fulfill that, you should get an option to form a new dynasty -- Capet-Holstein dynasty. All the lineal successors of King of Denmark will become part of this new dynasty. Now, the King of Denmark is the master of his own dynasty and free from the influence of the King of France. He won't have to pay any tribute, etc.
There should be some drawbacks. For example, the alliance between dynasties will not be present any more. Nor will you be voted by the parent dynasty under Tannistry or Elective succession laws. There could be some relationship boost between dynasty members. However, for player succession purposes, parent dynasty and it's cadet dynasty should be treated as one. It should not be game-over if your new dynasty is your cadet dynasty. Or, if you have formed your own cadet dynasty, it shouldn't be game over if your successor belongs to your parent dynasty.