Flight instructor on training flight with student reported an aborted take-off due to engine anomaly followed by a runway excursion.

Narrative

During pattern practice; flight instructor pilot was operating aircraft from right seat. Passenger who has had limited flight instruction occupied left seat as passenger. The aircraft does not have toe brakes on the right side; only a hand brake to apply braking to L&R simultaneously. This was briefed in advance between right-seat PIC (Pilot In Command) and left-seat passenger. Positive exchange of controls was discussed.After approximately six laps in the pattern; an unidentified engine 'anomaly' occurred. PIC perceiving unusual sounds and power loss; executed a rejection of the take-off from near rotation speed with around 2;500 ft. runway remaining. Left seat passenger assumed that pilot flying would need help stopping and attempted to apply brakes; but inadvertently applied heavy left brake. The plane swerved left; and full right pedal from right seat pilot flying was inadequate to correct. Perceiving that impact with a runway edge light was imminent; pilot flying applied left pedal to depart runway between two lights. Aircraft was brought under control in the grass; and taxied back onto the runway with no damage. Aircraft was taxied for maintenance inspection.Critically; a more thorough briefing of positive control exchange should have been conducted by flight instructor pilot. This should have included that no control inputs are expected from student/passenger unless directed. Knowing that critical events like rejected take-offs do occur; the flight instructor flying should have provided more time in taxi instruction prior to embarking on flight. Flight instructor will approach any future opportunity to operate aircraft without full dual controls with exceptional care and briefing.