As a professional, he played for the Detroit Lions of the NFL in addition to exhibition and training camp experience with the Seattle Seahawks, St. Louis Rams and Chicago Bears.
He also played for the Grand Rapids Rampage, Carolina Cobras, Milwaukee Mustangs, Los Angeles Avengers, and Dallas Desperados of the AFL.
Hamilton attended Spanish River Community High School in Boca Raton, Florida, where he was a three-sport athlete in football, soccer, and tennis.
Hamilton was named after the Rémy Martin brand of cognac, which his parents once served as owners of the New Jersey Bolero Motel and Bar.
[2] After making a 47-yard field goal in his only attempt as a freshman, he lost the kicking job to Erik Lovell in spring practice.
Lovell handled the kicking duties in the 1994 NCAA Division I-A football season opener and Hamilton did not get the starting assignment until immediately before the second game.
[5][6] Notre Dame called a timeout to ice Hamilton, but it inadvertently helped Michigan, which had prematurely packed away the kicking net on its sidelines.
[4] The field goal redeemed Hamilton for a missed tackle on a kickoff return, which he felt would have cost his team the game.
[2][11] Despite NFL alumni that include Jay Feely, Hayden Epstein and Ali Haji-Sheikh, Hamilton remains the school's only All-American placekicker.
[2] During the 1994 football season, Hamilton established the current Big Ten single-season record for successful field goals at 25, which has since been tied three times,.
[12] The Big Ten was talented at the placekicker position that season, with four of the twenty semifinalists for the Lou Groza Award being from the conference (Hamilton, Illinois' Chris Richardson, Minnesota's Mike Chalberg and Northwestern's Sam Valenzisi).
[7] His 14 consecutive field goals mark was one short of Vlade Janakievski's Big Ten record, which has since been broken.
[12] Hamilton's 63 career field goals were two short of Todd Gregoire's Big Ten record, which has since been broken.
[28] Following his strong performance, he signed with the NFL's Seattle Seahawks on August 4,[29][30] where he competed against rookie Josh Brown.
[31] After Brown was perfect in both four field goal and seven extra point attempts in the first three preseason games,[32][33][34] Hamilton was released on August 25,[35] and he returned to play for Los Angeles again.
[47] That year, he eclipsed Jay Taylor's AFL record for single-season field goal percentage, which had been 72%, with a 74.4% 29 for 39 performance.
[27] Hamilton started the season with eleven consecutive field goals, giving him a total of twelve in a row for a league record.
[55] He appeared in one NFL game for Detroit, but missed his only point after touchdown attempt,[56] which was blocked by Alfonso Boone.
[72] In a May 2009 article, the Los Angeles Times reported that, less than 15 hours after a 53–52 overtime loss to the Georgia Force at Staples Center, Hamilton's wife, Heather, delivered the couple's first child, a boy named Tate.