It's fairly obvious to the uninformed observer that tornadoes rotate, but I'm wondering when it became accepted knowledge that hurricanes did the same on a larger scale. I recall that the USS Wasp had an typhoon eye wall on radar in 1944, but that seems quite late as a possibility. Am I not giving our forbears enough credit?
I guess you can attribute the discovery of the rotational behaviour of hurricanes to the discovery of the Coriolis effect. The Coriolis effect is largely responsible for the rotation of large cyclones and it was discovered by Gaspard-Gustave Coriolis in 1835, but it was not used in the field of meteorology up until the early 20th century.
It was certainly known by 1922 with "Weather Prediction By Numerical Process". I'd argue it was also known before hand. I'm not sure if the rotational aspect might be observed in person as a ship travels to/from the center of the storm, but it's not terribly difficult to establish by induction that a) the center has a rotational aspect, easily observable by eye, b) from the perspective of both winds and (visually) by clouds does not have a clearly demarcated point at which the air moves in a non rotational aspect, that the entirety of the storm that is visible to a naked eye rotates around a (rough) center.
As to when we discovered the full size and shape of hurricanes, that was probably not available until at least the invention of radar. Before that, it would have been too dangerous and too slow to collect enough data to piece together anything like the atmospheric data we started to see in the early twentieth century.