PA-28 flight instructor reported experiencing spatial disorientation climbing through a cloud layer that resulted in a turn and descent that were quickly corrected.

Narrative

The weather reported for that day was a small layer from about 2;000-3;0000' AGL. My student and I reviewed a separate standard flight briefing on foreflight; and a standard briefing from 1800wxbrief via the phone before the flight as well. The decision to make the flight would not have been made if the real and actual conditions were known. The actual conditions were IMC from 2;000-6;000+ AGL. We picked up a clearance and pop up clearance with the Tower; and were in a plane certified for IMC; and I was current as the PIC. However; because the cloud deck was so thick; we were in IMC much longer then anticipated. As a result of being in IMC for an extended period of time; the PIC became disoriented and started a turn and descent. This turn and descent were caught within a minute; and the plane was restored to straight and level. The PIC then asked ATC for vectors and altitudes to VMC conditions; which were given. The PIC deemed it wise to return to the home airport due to the inclement and unforecasted weather. There was a hurricane ravaging through the country at this time; and the PIC has speculated that the erroneous forecast may be influenced by that; and the associated power outages nationwide.