The purpose of the flight was for both flight instructors to perform a proficiency flight with one another. After performing maneuvers in the practice area, they returned to the departure airport to conduct touch-and-go practice takeoffs and landings. After the right-seated flight instructor made two landings, the left-seated flight instructor conducted the landing. After touchdown, while the airplane was in the landing roll, the left-seated flight instructor manipulated the landing gear position selection lever to the "up" position instead of the flap lever. Both instructors realized the mistake and attempted to move the gear lever back to the "down" position, but the left landing gear had already collapsed. The landing gear continued to retract, and they became airborne. After performing troubleshooting of the landing gear and performing a flyby, they decided to land at another airport with more facilities. The right-seated flight instructor performed the landing at the alternate airport and the airplane rolled on all three landing gear for about 1,000 ft. The left landing gear then collapsed and the airplane veered off the runway. The left aileron sustained damage as a result of the gear collapse. The left-seated flight instructor reported that there were no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.