Sarah Palin’s three-year-old grandson has been filmed using a gay slur against his aunt in one of the family’s reality television shows.

Bristol Palin’s son Tripp, who features on her programme Life’s a Tripp, called his aunt a “faggot” when he was not allowed to use a swimming pool.

The Palins have engaged in a number of reality television shows since Sarah Palin’s role as Republican running mate for John McCain in the 2008 US presidential elections.

A trailer for the latest programme shows Bristol and her sister Willow arriving in Phoenix, Arizona. They check into a hotel when the child asks to use the pool.

His request is refused as they have been travelling. He tells his mother and aunt he hates them. Bristol Palin warns him, “God’s watching you,” as her sister threatens to wash his mouth out.

The boy then tells his aunt: “Go away, you faggot. I don’t like you.”

Both sisters gasp, cover their faces and laugh nervously. Without leaving the sofa on which they have been seated, Willow unsuccessfully attempts to force the boy to sit in another room before the trailer ends.

In a voice-over, 21-year-old Bristol Palin, whose pregnancy rocked her mother’s vice-presidential campaign says: “I’m doing a terrible job disciplining Tripp. I know he’s going to continue to push the boundaries and push the limits.”

In 2010, the same younger sister Willow Palin told a Facebook friend that he was a “faggot” and “so gay” after he criticised her mother’s reality TV show.