The pilot stated the flight was from St. Augustine, Florida, to Ft. Lauderdale Executive Airport (KFXE), Ft. Lauderdale, Florida. After Pahokee, he was radar vectored to KFXE for the ILS RWY 8. The ATlS changed from Tango to Uniform at Pahokee. The current ATIS indicated a significant weather change- winds at 150 9KT gusting to 20KT, 6SM, Rain, BKN 1200 30.03. I calculated the cross-wind component as runway 8, winds 150 at 9 KT, gusts 20-15KT, crosswind within the limits of the aircraft and my training. I intercepted the ILS at 2000 ft from 120 degrees. I gained sight of the airport's light at 1200 ft near PRAIZ. I followed the glide slope down noting dark skies south of the airport. I passed through light to moderate rain. On final I was at 80+ knots and 20 degrees flaps. I did not deploy full flaps as I wanted a bit more speed. The runway was 6000 ft. Prior to touchdown, I corrected for the crosswind by turning the ailerons into the wind and applying opposite rudder and holding the correction. When the right main wheel touched the runway, the aircraft was suddenly lifted in the air. I found the aircraft above the runway, heading ESE toward the ALPHA taxiway losing altitude. Fearful of a collision with aircraft on taxiway ALPHA or landing in the grass soaked barrier, I powered-up the aircraft-flying it off the runway, applying significant left rudder while maintaining level wings. I attempted to maintain a nose high attitude. While flying back to the runway, I impacted a few markers with the rear of the aircraft. Once over the runway again, I landed runway 8 approximately 1:30PM EST and taxied to Alpha/Bravo intersection and contacted ground. The pilot stated there were no mechanical failures or malfunctions to the airplane or any of its systems prior to the accident. The KFXE weather recorded at the time of the accident was winds from 130 degrees at 9 knots, visibility 5, thunderstorm and rain, clouds 2500 scattered, 5,000 broken, temperature 23 C., dewpoint temperature 21 C..