House Saud effectively consolidated its power in 1744 with the Diriyah agreement, in which Muhammed bin Saud won the support of Muhammed ibn Abd al-Wahhab in return for promising Wahhabi clerics complete control over all religious matters within Saud's state. Despite multiple invasions and occupations, this agreement is still on the books.
Though the family is too large to generalize, those members of House Saud in the highest echelons of power are markedly more progressive than the Wahhabis who still have near-absolute control over the nation's moral standards. The royal family largely wants to fulfill Abdulaziz ibn Saud's dream of making Saudi Arabia an influential world player, and realize that the clerics' strict adherence to medieval interpretations of Islam are holding the nation back (this is why the government-controlled media has made sure no one outside the country gets a good look at one of their famed public beheadings... they know it would embarrass them). But, at the same time, the royal family realizes that these clerics are really the only thing holding the country together. If they piss the clerics off, they will lose their support, and the same jokers who turned the terrorists loose on the United States could do the same to them.
Contrary to what some suspect, we aren't being played here... at least not by the government. They are basically walking a tightrope between doing what's in the best interest of the country (moving them forward into the global economy) and trying to satisfy a class of regressive, intolerant clerics who would rather the nation split back up into its respective tribes and retreat to the desert to subsist on dates and camel milk.
So, I think you'll find the Saud family wants the terrorists gone every bit as much as we do. As per the pact established between our nations near the end of the Second World War, the royal family relies on the United States for income and protection. Without that, they are totally fucked. The problem is, despite being pretty much absolutist, there isn't a whole lot they can do about it, because, as noted, the clerics command greater respect from workaday Saudis than does the government.