DRG FAM FLT, CFI NOTED FUEL QUANTITY LOW WITH SELECTORS ON AUX FUEL TANKS. DRG ARC TO ILS APCH, CFI ALLOWED THE RT ENG TO FAIL DUE TO FUEL STARVATION. CFI SELECTED MAIN TKS AND OBTAINED RESTART. APCH WAS CONT TO A TOUCH AND GO LNDG PERFORMED BY THE ATP PLT RECEIVING INSTRUCTION IN THE LT SEAT. AS PWR WAS ADDED, THE ACFT DRIFTED TO THE RT, DESPITE THEUSE OF FULL LT RUDDER. THE CFI DID NOT ABORT THE TKOF BECAUSE HE THOUGHT SWERVE WAS EITHER PLT INDUCED OR DUE TO ASSYMETRICAL PWR FROM MISMATCHED THROTTLE CONTROLS. NEAR THE RT EDGE OF THE RWY THE CFI TOOK CONTROL AND ROTATED. HE RPTD THAT ROTATION OCCURRED AT 96 MPH AND THAT HE EXPERIENCED LT ROLLING FORCES IMMEDIATELY AFTER BECOMING AIRBORNE. THE LT SEAT PLT RPTD THE SPEED TO BE 80 TO 90 MPH. THE CFI FEATHERED THE LT PROP SHORTLY BEFORE IMPACT IN A LAKE. THE RT ENG TEST RAN SUCCESSFULLY. THE LT ENG WAS DISASSEMBLED REVEALING NO MALFTNS. RT PROP DISASSEMBLY INDICATED LITTLE PWR AT IMPACT. THE LT SEAT PLT SAID THERE WAS NO FORMAL PRE-BRIEF AND THAT THE FUEL SYSTEM WAS NEVER EXPLAINED TO HIM.