A different Salem bin Laden, (OTL patriarch of the bin Laden family untill his mysterious death in 1988), who, as well as people a well-connected corporate bigwig, has an interest in populist, Islamist politics. He spends most of his life kowtowing to the ibn Sauds untill some crisis strikes Saudi Arabia, at which point he oppurtunistically leads a palace coup, sponsored by sectors of the military and the general public. The Saudi dynasty is overthrown and the bin Ladens usurp the throne.
Osama, meanwhile, is off winning glory in Afghanistan. As the Soviets withdraw, Osama returns home, much to the delight of his family and his cousin Salem. He is promptly rewarded a number of high status government positions, including ambassadorship to the United States. During his career, he becomes well known and well respected.
On the 11th of September, 2001, Salem bin Laden dies of natural causes, and the campaign to decide upon his successor begins. Osama, with his natural charisma and Jihadist credentials wins many allies, and, importantly, the bulk of natural support. By the end of the month, Osama has emerged as the unquestioned new leader of the Kingdom - however, he refuses the royal title and instead declares a republic, the Islamic Republic of Arabia, with himself as president. Osama's modernising reforms are applauded in the West, especially as in 2003 he organises the state's first free legislative elections.
US President Bush and Arabian President bin Laden are well-acquainted and share a common foreign policy vision, particularly in containing and combatting Iran, (through maintaining the status quo with Iraq and supporting the anti-Iranian activities of the Taliban). In 2005, bin Laden's Arabia becomes one of the major contributors to the American-led invasion of Syria, (to liberate Lebanon, to remove an Iranian client, etc.).
Among quarters of right-wing America, Osama bin Laden is highly regarded as a loyal ally. He is jovially known as Uncle Osama, (emphasis on the 'sam'), on Talk Radio and throughout parts of the Internet. The same phrase is often picked up by those who lean to the left and used with irony, as Uncle Osama's government's committment to democracy is seen as only skin-deep and his support for regimes like the Taliban is reviled.