Instructor pilot reported violent flight control fluttering after takeoff and elected to land on the remaining runway rather than chance a flight around the pattern. The aircraft had been deiced prior to takeoff.

Narrative

During the pre-flight; there was icing observed on the control surfaces that was carefully and thoroughly removed. The icing was a result of rain from the previous day that had frozen over night. I would like to emphasize that all of the ice was removed during the pre-flight phase.During takeoff; after rotating and becoming airborne; and while increasing airspeed; there was a violent fluttering of the flight controls observed that negatively affected the controllability of the aircraft. The effects were severe enough that I do not believe that we would have been able to successfully complete an entire lap in the traffic pattern to land back at the airport. Fortunately; the runway was long enough that we were able to make a successful landing on the remaining runway and terminate the flight without further incident.It was concluded after the flight that the most likely cause was that some of the rain from the day before had made its way into some of the flight control surfaces and caused the fluttering once we reached a high enough airspeed for the imbalance to cause the fluttering. After temperatures warmed up above freezing; the airplane was flown again without issue.My biggest issue with this occurrence is that there is really no way to check for icing inside of the control surfaces on any airplane that I have ever flown. As far as I'm aware; the only way to detect this issue is to fly the airplane and observe the fluttering. Proper corrective action if this is observed in the future would be to abort the takeoff; if able; and if unable to abort; reduce to an airspeed that prevents the fluttering and return to land at or below that particular airspeed.