C172 Instructor pilot reported a rough running engine and divert to a nearby airport.

Narrative

I was on a training flight with a student practicing maneuvers in the practice area south of ZZZ Delta airspace when the aircraft began to experience severe engine roughness. With ZZZ being the closest airport we made the decision to [request priority handling] and get clearance to land at ZZZ airfield. Once we had landed safely and gotten clear of the runway; we exited the aircraft and began to talk with the airport manager about what action to take next. After talking with the airport manager; she advised me to call my boss (the owner of the flight school and head of maintenance). While on the phone with him he told me to get in the aircraft and instructed me to run the engine up to full power for a few minutes to burn off any possible spark plug fouling. Afterward; he had me do multiple magneto checks at different RPMs to test if the problem had been fixed. Upon doing the tests; the engine was running smoothly again. After informing him that the problem had been fixed; my boss; who is also an A&P/IA; advised me to fly the aircraft back to ZZZ1 airport. From there I discussed with the airport manager and my boss as a group what action to take next. My boss told me that he informed that I was cleared to takeoff to return the aircraft to ZZZ1 airport as long as it was only me aboard the aircraft.The airport manager discussed with the tower who also said I was cleared to depart. At this time my boss made it seem to me like this was the correct thing to do to bring the aircraft back and I felt pressured by my boss and did not want to go against his instructions. Then two days later after my chief instructor contacted me about the situation he advised me that I had taken the wrong course of action and should have never departed the airport. After reviewing the regulations I now realize that I did not follow the proper protocol. I learned that as PIC I should not have let anyone influence my decision to fly or not to fly no matter what implications it may have. Going forward I am going to make a better effort to create a better safety culture and encourage my fellow instructors to never fly no matter how pressured they may feel by external pressures.