The tussle between the brothers and the policeman was caught on video by a number of bystanders.
Video footage shows one of the men holding down the officer, while taking the gun and passing it to his brother standing next to him.
The officer kicks at the man, using his legs and one of his arms to try and free himself.
Near the end of the video the man can then be seen holding the officer in a head-lock before lifting him up off the ground.
One woman can be heard helling “stop” in the background of the video.
“The police man was trying to attack us,” one of the brothers responds.
Nearby officers then rushed to the scene, where they arrested both men.
The pair face multiple charges including bribery, robbery and obstructing police.
Both brothers denied all charges, Associated Press reports, and Phuket provincial police chief Sinlert Sukhum said police will request the court to deny their release on bail.
According toThe Bangkok Post, the brothers entered Thailand on March 11 and were granted permission to stay until April 9. Visitors from New Zealand are allowed in Thailand for 30 days without a visa.
Rebecca Day told the Herald she was running on adrenaline and was struggling to sleep. She said she is trying to stay strong for her son Jake.
“I cry in my quiet times and when I get a spare moment – after dropping Jake at school or in the shower.”
“What is our son going to do? Boys need their dad. There will be some things where I will try my best but I can’t replace his dad, as much as I will give it everything,” she told the Herald.
“I just want to get him home. And I just want Jake to have his daddy again.”