The pilot reported that during his pleasure flight he performed three off-airport takeoffs and landings. During his last landing, a main landing gear wheel separated from his amateur-built twin-engine airplane when an attachment weld sheared. When the pilot subsequently landed back at the airport, he was unable to maintain directional control of his airplane. The airplane impacted objects, and the right side of the fuselage buckled. Witnesses reported that they were located on a river raft and observed the accident airplane flying 100 feet overhead. The airplane appeared to touchdown on a sand/gravel bar that was within 75 yards of their location. During this event, one of the airplane's wheels separated and initially traveled toward them, but then veered away and entered the river. Thereafter, the pilot "gunned his engines" and overflew the raft while circling the area.