Crusader Kings 2 – How to Handle Threats for Being a Ruler?

Open up your character window, and hover your mouse over your titles. An infobox should now appear, showing you the name of the title, the succession law and the line of succession.

I do not know a way to change the laws other than the one for your primary title, however. :/

EDIT:
Ok, I think I understand now. I believe it the core of the answer is whether or not a title is a de jure vassal to one of your greater titles. The succession law of a title will always be determined by the greatest title you hold in that "realm". If you have titles in other "realms", those will be determined separately.

• For example, if you are King of Ireland and the Duke of Munster (which is de jure part of Ireland), then the duchy will inherit the succession law of the Kingdom of Ireland.
• However, if you are also the Duke of East Anglia (de jure part of England), then that duchy will have its own succession laws.
• If you also hold the title of King of England, then the duchy of East Anglia will inherit its succession laws from England (which are separate from the succession laws of Ireland, even if you hold both titles).
• Now, if you also happen to be Emperor of Brittania, then I assume all the titles from within that realm inherit the succession laws from your primary title.
• Should you hold titles which are not de jure part of Brittania (say, King of Poland), then those will have their own laws, and the chain will start over from count to emperor, depending on your greatest title within that "realm".

PS: I know my use of the word 'realm' may be a bit different from the one used in game, but I could not find one that fit. What I mean by "realm", is a collection of titles which are de jure connected under one greater title which you control. I hope my intentions comes across despite this.

Succession laws for multiple kingdoms (and no emperor title)
(For your example where you are the King of Ireland and Wales)

1. King of Ireland and your lower titles that are de jure part of Ireland are governed by the succession laws for "King of Ireland".
2. King of Wales and your lower titles that are de jure part of Wales are governed by the succession laws for "King of Wales".
3. [Duke and lower] titles that are not de jure part of any of your King titles are governed by the succession laws for your primary title

Changing a succession law
If you changed the succession law for King of Ireland, and King of Ireland is your primary title, all of your de jure Irish titles and titles outside any of your de jure kingdoms (#1 and #3 above) will be governed by the new succession law.

You would need to change King of Wales separately. (In the law interface, click on the coat of arms for Wales.)

Succession laws for titles held by vassals
Your vassals have their own separate laws for succession which could be totally different from yours. For example, you have have agnatic primogeniture as your kingdom succession law, and your vassal duke could have agnatic-cognatic gavelkind as his succession law.