Folks at Larry Flynt's Hustler Club in Las Vegas tell TMZ ... Aubrey threw a fit Monday night when a bday cake was carted out for the Prez's son after she finished her 3-song set.

We're told she was pissed because she was asked to sing "Happy Birthday" to her former fling -- which was allegedly not part of her contract -- then one of her assistants got physical with a cocktail server.

We got video of the ex-Danity Kane member being escorted out after her performance, seemingly at the direction of one of the club's managers who shouts at her to leave the building.

We broke the story ... the New Year's Eve bash was a total troll job by the club, because Larry Flynt famously hates President Trump. Having it hosted by his son's alleged ex-mistress was part of the joke.

Seems like O'Day was tired of playing along though.

We reached out to her ... no word back so far.