Surasak Suwanchot, 26, originally from Nakhon Sri Thammarat, who is accused of stabbing Mrs Smith, and Surin Tapthong, 37, originally from Sumat Sakhon, accused of driving the motorbike involved, performed a re-enactment yesterday and were later taken to Phuket Town.
Police said they have confessed.
Today the court ordered them detained without bail until the prosecution case against them has been compiled.
The pair performed the re-enactment yesterday in Kata Noi, in front of a large crowd.