The pilot stated that, after a local pleasure flight with his children as passengers, he returned to his departure airport and re-entered the traffic pattern for runway 22. He reported that while on final approach he didn't like the way things looked and chose to go-around. He stated that initially the aircraft responded normally and began to climb, but 'immediately after metering off flaps, the engine began to vibrate grossly out-of-balance.' The pilot performed emergency procedures, but the 'loss of power and altitude continued....lake landing was very suspect due to lack of altitude. Reviewed area for alternative - none!' The aircraft struck the top of a large tree and then contacted a smaller tree before it descended into the lake. Pilot and passengers were able to exit the aircraft before it sank. The aircraft was submerged for more than 20 hours before it was recovered from the lake. A subsequent engine run-up was satisfactorily accomplished.