"Shotgun unity" is a play on the phrase "Shotgun marriage," which describes a marriage that was compelled or forced. It comes from the days when out-of-wedlock children was a substantial social stigma and the sire was expected to become husband, even if it had to happen at the point of a gun.
Thus, "shotgun unity" describes a compelled or forced unity: one that neither party particularly wants, but are forced to endure due to a more demanding need.
Note: your suggestion that it might be related to "shotgun approach" is in error as the use of "shotgun" in that regard refers to the spread of the pellets vs. the power of the gun. By throwing a lot of pellets into the air, it's easier to hunt a bird compared to using a single-shot (e.g., a .22 caliber rifle) weapon. Thus, a "shotgun approach" refers to using many different, simultaneous solutions to guarantee achieving a goal.