On August 9, 2002, at approximately 1345 mountain daylight time, a Cessna 310N, N111KC, was substantially damaged during a hard landing at Glenwood Springs Municipal Airport (GWS), Glenwood Springs, Colorado. At 1456, the airplane was further damaged during an intentional gear-up landing at Walker Field (GJT), Grand Junction, Colorado. The airline transport pilot, and the pilot receiving instruction, were not injured. Visual meteorological conditions prevailed. No flight plan had been filed for this instructional cross-country flight being conducted under Title 14 CFR Part 91. The flight originated at Pueblo Memorial Airport, Pueblo, Colorado, at approximately 1245. According to the instructor, the pilot receiving instruction made a hard landing at Glenwood Springs. The instructor took the controls and initiated a go-around. Suspecting landing gear damage, he kept the landing gear extended and diverted to Garfield County Regional Airport (RIL), in Rifle, Colorado. On the approach to Garfield County Regional, the right main landing gear fell off the aircraft. Because of the limited emergency equipment at Garfield County Regional, he was advised to divert to Walker Field, in Grand Junction, Colorado. While keeping the landing gear extended, they made a low pass over the runway at Walker Field, and witnesses confirmed the missing right main landing gear. The instructor retracted the landing gear and made an intentional gear-up landing. The airplane sustained extensive damage to the lower fuselage skin and bulkheads and substantial damage to the right main landing gear attachment point.