Being as the differences between the QC Universe and our own are largely technological with no change to the music scene or the cultural forces that affected the progression of musical trends, the split must have happened relatively recently. The limiting factor would have to be that the split happened early enough to produce a space station suitable for families in time for Hannelore to be raised on one. As Hannelore is in her early to mid-20s, this would have had to have occurred some time in the 1980s. Based on that, I think I've got a chain of events that would work. Witness:
In the mid 1980s, Steve Jobs saw that while the Mac had a good grip on colleges the PC was seizing the workplace. Jobs retooled the Mac OS with a unix base and a mandate to make the Mac compatible with a DOS office. Compatibility was the new paradigm. By doing so, Apple never stopped being a major player in the PC market. This kept the heat on Microsoft and Sun, forcing them to keep innovating. In order to get an edge, Apple formed an early partnership with AOL. By introducing the internet to Mac users (and specifically college-age Mac users), the left embraced online political organizing early enough to make a difference in the 1988 Presidential campaign. The result was that Michael Dukakis was elected President instead of George H. W. Bush.
In 1990, Senator Al Gore was in Saudi Arabia on an official visit to meet with Bandar bin Sultan, the Saudi Ambassador to the United States. While there, he met with Salem bin Laden, eldest of the bin Laden brothers and CEO of the Saudi Bin Laden group and was introduced to Salem's half-brother, Osama bin Laden. Osama, a considerably more religious man than Salem, made some comments to Gore which were considered less than polite and were not translated. This led to an argument between the brothers and they adjourned to another room. Once in private, Osama slapped Salem across the face and told him he had disgraced the family and all their late father had built by consorting with an infidel. This led to a full-fledged screaming then wrestling match between the cousins. In a repeat of the 1963 Battle of Ramadan, the match ended with Salem sitting on Osama's chest with his arms pinned. Rather than playing another round of "stop hitting yourself", Salem explained to his brother that the relationship between the bin Laden family and the Bush family was what had brought them wealth and power and that building business relationships with Westerners was their father's greatest accomplishment. Salem then explained that these relationships played a major factor in spreading Islam to the West and that segregating themselves from the West would only keep the word of the Prophet from western ears.
Humbled at the strength of the argument and the rebuke from his eldest brother, Osama apologized to Salem, returned to school, earned a broadcasting degree and went to work for Al-Jazeera. His program, "Osama", soon became the most popular daytime talk show in the Arab world, blending religious discourse with interviews, entertainment news, sports coverage, politics and health issues. In 1989, bin Laden began a campaign against Iraqi dictator Saddam Hussein sparked by reports of Hussein's use of chemical weapons against Kurdish Iraqis during the Iran-Iraq war. Bin Laden offered a pan-Islamic vision, stating that while there were Kurds, Shiites and Sunis, the people of the Middle East were first and foremost Muslims and that the genocide was a crime against not only humanity, but against Allah. In a 1991 ceremony at the UN, Osama bin Laden was honored for his contribution to Iraq's "Velvet Revolution" that removed Saddam Hussein from power.
With a US economy booming from cheap gas, the Peace Dividend brought on by a radical reduction in military spending at the end of the Cold War and a more stable Middle East was directed to technological research in an effort to keep former defense workers employed. in 1992 a young hardware engineer at Apple, William Ellicott, developed a new method of cooling chips. Excited by his accomplishment, he told his wife, Inga Chatham who was working on battery technology for Apple. Dr. Chatham had worked out a new system that increased the amount of power that could be stored on a battery of a given size by a factor of 10,000. Her problem was that the battery generated so much heat that the extra power was given over to cooling for a net gain of 0. Armed with the two complementary technologies, Drs. Ellicott and Chatham poured themselves into their own private skunkworks and in a 30-day work-binge created a prototype of the first AnthroPC out of seven Newtons and 10,000 Legos.
The initial demonstration of the AnthroPC was a rocky affair. "Baldrick" demonstrated a certain degree of mobility and his voice recognition was passable, but he required a significant amount of prodding to complete the demonstration tasks. Furthermore, Baldrick's hacked-together appearance did nothing to impress Steve Jobs' hypercritical design sense. He was unimpressed and launched on a tirade about half-baked design, its inability to accomplish basic tasks and the inherent ugliness of the prototype. As Steve ranted, Baldrick walked over to a box of Legos and began to re-assemble himself. He removed some of the bricks from his legs and used them to lengthen his arms, added a second elbow joint and a tail he could use as a stabilizer while walking up ramps and started the demonstration course again.
At this, Jobs was agog. He stared at Baldrick, now zooming through the course at record speed, with an expression somewhere between wonder and rage. He turned on Ellicott and Chatham who were equally stunned and demanded an explanation. "Are you fucking with me?!", Jobs screamed. Ellicott and Chatham, now wondering the same thing, were speechless and began looking around for someone with a remote control. Baldrick, seeming to sense the situation, returned to the Lego bin and pulled out more some parts. He walked over to Jobs, stopped, and looked the CEO in the eye. Then Baldrick changed the world: he reached into his storage pouch, pulled out a small Apple sticker and placed it proudly on his chest.