This is a question I've been wondering for a while now as well. So far, I've only had one game, House Mudd of The River and the Hills (Riverlands), where I had the ability to pick that ambition. I have no idea how the option was suddenly available. I then looked at some possibilites as why this might be possible to achieve.

On that note, I do not believe the ambition is only available to certain houses. I've seen both House Vance of Wayfarer's Rest and House Wyl of The Boneway get the ambition to become King of [Region]. They are not of significant Houses. I also do not believe Religion/Culture, Combat skill -Master/Novice, or the trait you get when you become of age - Brilliant Strategist/Underhanded Rouge, has any effect as well.

From all the rulers who have had the ambition: They were all scholars (I don't think this matters), and they all had the ambitious trait. I'm 90 percent certain that this has some sort of significance. All these characters are also between 30 and 50. I know that eventually you get too old to pick the improve combat skill ambition, so I theorize that you can only get the become King of [Region] sometime in your thirties. My last idea is that you need 1,000 prestige. This is because you need this amount before you can start subjugating. Other that that, I have no idea how you get the ambition. Hope this helps get a starting point, but I hope someone actually has the answer :P

There are specific requirements for your character to get these to show up as an option. I am off my computer right now, but I can post where to find them in the files later.

I would love to know this -- I need a clawman to rule over the Dusklands

You need to be:
-landed
-a king
-independent
-ambitious
-not incapable
-martial = 12
-stewardship = 10
-diplomacy = 9
Your capital needs to be in the specific region and the high kingdom must not have a holder.

Thank you!