KATE GOSSELIN brought her 13-year-old twin daughters Cara and Mady on the "Today" show yesterday to do damage control . . . and things didn't go exactly as she'd planned.

Kate wanted the girls to dispel rumors that their home life is totally screwed up, but even when they were asked direct questions, they REFUSED TO TALK.

Kate seemed pretty humiliated.  At one point she even told her daughter, quote, "Mady, your words.  It's your chance . . . spit it out." 

Kate's attempt to goad the kids into talking while clearly holding back a tidal wave of anger and embarrassment were PRICELESS.  When Mady did finally talk, she cleared things up a little.

The girls were asked if people have the wrong impression of their family, and she said, quote, "I wouldn't say 'wrong', I would just say not, like, the full story."

She added, quote, "A lot of people think that filming our show has damaged us, but it’s only really helped."  And both girls said they'd like to do another TV show.