does any body know if there is any public transport from baden airpark to hotel haus reichert Sophienstr.?
Bus 285 will take you from the airport to Baden-Baden Bahnhof (railway station). Timetable here:
From there you could take a taxi to your Baden-Baden hotel (it's about 3.5 miles) or any of several local buses to Leopoldsplatz (a minute or so's walk from the hotel). Bus route map: