A COMPANY DESIGNATED INSTR AND TWO F/O TRAINEES WERE CONDUCTING A FAR 135 TRNG FLT. THE THIRD APCH WAS TERMINATED WITH AGO-AROUND INITIATED OVER THE RWY THRESHOLD AT ABOUT 50 FT. AFTER CLIMBING TO ABOUT 150 FT, THE ACFT WAS OBSERVED TO OSCILLATE IN YAW, FOLLOWED BY PITCH, AND THEN ROLL TO THE RIGHT. THE ACFT IMPACTED IN A NEAR-VERTICAL DESCENT ATTITUDE. THE INVESTIGATION REVEALED THAT THE RIGHT ENGINE WAS OPERATING, BUT AT REDUCED POWER. THE LEFT ENGINE WAS AT FULL POWER.THERE WAS NO INDICATION OF ACFT SYSTEM MALFUNCTION OR FAILURE. COMPANY PILOTS INDICATED THAT THE CAPT HAD A HISTORY OF DEMEANING COCKPIT BEHAVIOR AND ROUGHNESS WITH STUDENTS. THE F/O, WAS SMALL IN STATURE AND HAD 100 HRS OF MULTI-ENG TIME AND NO TURBOPROP TIME. COMPANY PILOTS REPORTED THE F/O TRAINEE WAS CONSISTENTLY BEHIND THE ACFT IN PRIOR FLIGHTS. EXAM OF THE ACFT REVEALED THE FLAPS IN THE RETRACTED POSITION CONTRARY TO ACFT HANDBOOK. COMPANY PILOTS FURTHER INDICATED THE CAPT HAD HISTORY OF REQUIRING LOW ALTITUDE 1-ENG GO-AROUNDS AND DELAYING OFFERS OF ASSISTANCE TO STUDENTS.