In this ATL, the V2 is developed to the point where it capable of striking US targets.
Development of the V2
After it was found out that the V1 Flying Missile was too easy to intercept, Adolf Hitler ordered the development of the V2 missile. Unlike the OTL, the tests were all successful. The test targets were abandoned concentration camps still full of Jewish prisoners. 2 tests were conducted.
Meanwhile, several German spies managed to steal Albert Einstein's research on nuclear fission. The result: no Hiroshima & Nagasaki bombings.
End of Democracy
The very first official launch was at London on January 27th, 1944, with a launch of 5 missiles. Over 100,000 civilians & military personnel were killed & Big Bens Clock was destroyed, de-moralizing the British Army.
Hitler was delighted by the news, so much that he ordered a launch on an American target on July 4th, 1944. When news of the attack reached the White House, President Franklin D. Roosevelt knew that the Allies were out of time.
Hitler selected New York City as the target. The V2 was shipped to the launch pad at 10:31 AM Berlin Time. The launch was scheduled for 12:00 Noon Eastern Time. With the timezones working against them, pad crews worked quickly to get the missile fueled & loaded with the ordnance. One of Hitler's scientists loaded an atomic warhead instead, at Hitler's request. The missile was launched at 11:00 PM Eastern Time.
The USA set up a V2 Missile Defense Network. At 11:20 AM EDT a monitoring ship detected the V2 Missile over the Early Warning Line. The report reached the White House at 11:25 AM EDT. President Roosevelt ordered a launch of all bombers stationed in Europe to sweep over Germany & find Hitler. Meanwhile, Hitler contacted Hideki Tojo to start invading the US West Coast. The Japanese Fleet, under the command of Naval Marshal General Isoroku Yamamoto, mobilized at 4:00 AM Tokyo Time.
The V2 impacted New York City at 12:00 Noon EDT. Over 500,000 civilians were instantly killed, with another 360,000 in the following hours. Over 1,000,000 were injured. Roosevelt addressed the nation at 8:30 PM EDT, saying that Hitler had went too far.
Meanwhile, Hitler sent a message saying that more attacks will follow unless control of the US government is transferred to him. Roosevelt denied the request...just as the bombers began hammering Berlin. Hitler was never warned of a counter-attack. He immediately ordered a massive salvo of 50 Nuclear V2's be launched at American, British & Soviet targets.
The missiles hit between 9:00 & 11:00 PM UTC. Most of the population in the USA, UK & USSR were wiped out. However, several missiles flew errant & hit Berlin, Rome & Tokyo, effectively destroying both the Allies & the Axis.
Having zero knowledge of fallout & radiation, the world population was reduced to 10,000 in days. The surviving population was reduced to tribes of savages, who were out to kill each other. By 1950, only 500 humans were still living.
In 1990, the last humans died of old age, effectively ending the rule of man. Only cockroaches survived the radiation, but without a food source, they too died soon. By 2000, all of the Earth's atmosphere had boiled away, all signs of life were gone & the last remnants of civilization were buried by erosion.