Kate Gosselin -- Twins HUMILIATE Her on Live TV

Kate Gosselin's attempt to show how great things are going for her kids blew up in her face on live TV this morning ... because the kids CLEARLY didn't follow the script.

Kate appeared on the "Today" show with her 13-year-old twins Cara and Mady ... they were SUPPOSED to talk about how their mom has raised them as normal teenage girls who haven't been damaged by being on a reality TV show.

But when the cameras went on ... the girls refused to perform in Kate's dog-and-pony show ... and Kate was clearly PISSED.

"It's your chance ... spit it out," Kate demanded.