JetBlue gave a family the ole heave ho off a flight after a dispute with flight attendants over birthday cake … that left 2 little kids in tears.

The Burke family was flying out of JFK Airport to Las Vegas earlier this month when things got heated. According to Cameron Burke — who shot video of the incident — he and his family had the cake as carry-on. It was special ordered to celebrate his wife’s 40th.

The Burkes say a flight attendant first argued with them over whether to place it in overhead or under the seat … and then another attendant arrived and said it couldn’t be on board at all. Cameron says that 2nd attendant, the “mean” one told him he was being “non-compliant” when he attempted to calm things down.

He admits he asked her, “Have you been drinking?” — because he felt she was being erratic and irrational about a cake. In the video, you can see the Burkes kids getting upset … especially when police showed up.

Officers escorted the Burkes, who went peacefully, off the plane. A JetBlue spokesman told ABC7 – which first reported the story — the Burkes were yelling and cursing at the crew, and disruptive.

Cameron denies that, and says he’s already talking to attorneys about filing a lawsuit.

BTW, they re-booked their flight to Vegas … on United.  They did NOT bring the cake.