Last week, Sarah Palin shot a caribou; this week, Sarah Palin might have, at the very least, used a taser gun on Kate Gosselin and I doubt that even Aaron Sorkin would lodge so much as a complaint.

The idea was a TLC match made in heaven, or hell: Put its two biggest stars, Palin and Gosselin, in one episode of Sarah Palin’s Alaska. In theory, it made sense. Gosselin is always looking for ways to get out of the house with her eight children and her deeply bitter single-motherhood. So why not fly the brood up to Alaska, roll the cameras, and watch the fun as the two Mama Grizzlies compare media battle scars?

In practice, however, the hour was a remarkable, surprising, tedious catastrophe. The episode started out ordinarily enough. Sarah visited a gun shop to ask, “What’s the best bear gun?” She turned to the camera and explained sunnily that in Alaska, “guns are as common as bein’ in New York City and somebody with a Blackberry on their hip.” (You can untangle that grammar easily enough to figure out what she meant.) She went home and told daughter Piper that Kate Gosslin and her children were coming, informing us that “Piper is a big fan” of Kate’s.

So far, so good. Then the Gosselins arrived in Wasilla. Kate told us that she felt she had common ground with Palin, that here was someone who “can understand the scrutiny and the media” that have become Kate’s crosses to bear. Speaking of bear, Kate was immediately taken to a class in how to survive a bear attack while camping (“Learn To Return” is what the lesson was called). Kate looked apprehensive, as might any city or suburban dweller in what Palin always likes to call “the lower 48.”

Then the trouble started. Or as Sarah’s father said later of Kate, “She bitched from the moment she got off the plane.” The morning of the camp-out, it began to rain. “I’ve never camped for real,” said Kate, gazing at the damp camp site that had been chosen. “You really like this?” she asked Palin. Sarah maintained high spirits in direct proportion to Kate’s plummeting spirits. “We’ll stoke the fire and stoke some fun!” Palin crowed, bustling around with Piper, daughter Willow, and many of the Gosselin children gathering sticks and chunks of wood.

Kate, however, left her brood to the care of Sarah and Palin’s dad. (Husband Todd, wise man that he is, very noticeably went off to fish somewhere where he would not be able to hear Kate’s lamentations.) Kate jammed her hands in her poncho pockets, parked herself under a small open canopy that had been built for minimal rain protection, and started to complain.

“I’m worried about my toes; they’re freezing,” she said.

“I’ve been bitten [by bugs] about 200 times — it’s horrible,” she moaned.

“I’m miserable, but somebody‘s gotta be,” she said nonsensically.

“This is cruel and unusual punishment,” she whined.

When Palin and her daughters helped all the little Gosselins make s’mores over the camp fire, Kate declined to join them. Instead, seeing some gooey marshmallow land on a few sleeves, she went into a temper-tantrum fury.

“This is ridiculous!” she shrieked. “I just don’t get it! There are no paper towels! I’m freezing to the bone, I have 19 layers on, my hands are frigid!”

Kate issued an ultimatum: “I held it together as long as I could, and I’m done now.”

And she told the kids they were not going to camp out overnight as planned; they were heading back home. Their little faces fell. They hesitated and expressed little chirps of protest, saying they wanted to stay.

Kate was cruelly decisive: “Okay, goodbye. You’re now a Palin, not a Gosselin,” she said. Faced with a camp-out versus a loss of identity, the wee ones followed their mom onto a waiting plane to escape Alaska. Cut to an appalled-seeming Piper, who no longer looked as though she was a fan of Kate’s. Palin and her family remained, and spent the night in tents.

Palin said she regretted only that the Gosselin children missed out on the camp-out, a “good experience they never would have forgotten.”

I honestly cannot imagine what goes through Kate Gosselin’s head these days. Why does she voluntarily place herself in situations in which she knows she’ll end up in a foul mood, and then not even try, even if only for the selfish reason of improving her media image, to be minimally pleasant? Since every one of Kate’s complaints was made directly to the camera, no one can even claim that the producers of Sarah Palin’s Alaska somehow edited the footage to make Gosselin look bad.

She did that all on her own.

Did you watch Sarah Palin’s Alaska this week?

Twitter: @kentucker