I can only recall having had 3 events in light aeroplane instruction which required a prompt return to the aerodrome:
1. During a student's slow roll, engine oil spread itself across my side of the windscreen. As PIC, I took control; left all engine levers alone and used the available thrust to climb towards the aerodrome overhead, then set the throttle to idle and landed off a forced landing pattern. I also operated the radio as I wanted to make it clear to ATC that I would be requiring priority!
2. During departure with another student, I experienced a rough running engine at normal power / rpm settings. Again as PIC I took control, turned for the aerodrome overhead, found a power setting which allowed the engine to run 'normally', then told ATC my requirements before landing off a forced landing pattern.
3. Suction pump failure during the nav section of a PPL Skill Test. After confirming it was the pump, not the gauge, I told the student that the flight was a freebie for which he wouldn't be charged, then flew back to the aerodrome whilst he enjoyed the view.
If I was flying as PIC in a single engine aeroplane with an abnormal or emergency event, I would always take control and proceed as if solo rather than having some distracting discussion with the student, or risking him/her confusing ATC with poor RT. He/she would spend 100% of the time looking out for other traffic and we would debrief the problem only when safely on the ground.