Hours after the Saudi execution of a Shiite cleric that has set off a diplomatic crisis in the Persian Gulf, the two leaders of the Saudi royal family’s younger generation took in a horse race at the Janadriya track outside the capital. The appearance by Crown Prince Mohammed bin Nayef and his cousin, Deputy Crown Prince Mohammed bin Salman—who are partners and rivals—was an important show of unity at a critical moment. The crown prince is next in line to the throne. The deputy crown prince, two decades younger and second in line, has become such a hard-charging force that it has caught Saudi allies off guard and even caused grumbling from inside the royal family. The pair of princes are confronted by an array of challenges: a new terrorist threat in Islamic State, plunging revenues as oil prices swoon , a region in disarray—including from its own engagement […]