What did Frank and Claire realize after watching Governor Conway's video?

Question

At the end of Season 4, Episode 7 of House of Cards (Chapter 46), we see Claire lying in her White House bedroom late at night talking on the phone with her husband, who is also lying in his bedroom across the hall.

She tells him to go on Governor Conway's website, where he recently uploaded all of his personal photos and videos in order to cleverly reverse the public opinion's perception about his partnership in the Pollyhop scandal, and check out a video of 2013 New Year's Eve.

The video shows Governor Conway and his 7 months pregnant wife Hannah enjoying themselves at a Democrats (?) party attended also by Frank and Claire. The video images shortly turn into a flashback memory told from Frank's point of view in which we see Frank and Conway meeting for the first time.

During this conversation we come to learn Conway's true nature when Franks skeptically asks him if it is true that he enlistend right after 9/11, to which he responds:

"You want a career in politics and the Twin Towers fall in your lap? The timing couldn't have been better"

So, after getting to know throughout the whole episode the public and private side of this Republican "golden boy" who's gained an incredible credit in the public opinion also by parading his enlistening tale to show that he fought for his country, just like his grandfather did and unlike Underwood, we finally learn that he might just be a younger version of Frank, just as ruthless and cynical (and by the way if you look at Frank's smile after he's heard this revelation, he seems to be very pleased about it).

Shortly before this flashback, when commenting on the Conways, Claire admits to Frank that they are (the are the image of) the perfect couple: young, beautiful, with two kids, and that the Underwoods could never hope to match them in the eyes of the public opinion. But, as Claire states, the Underwoods have something that the Conways don't:

"We are willing to go one step further than everyone else"

Since we now know that the Conways are not this boyscouts couple/commercial family that they publicly project (and Frank and Claire should be very aware of that), why at the end of the episode and after watching the New Eve's clip are Claire and Frank so sure that they are going to defeat the Conways?

Claire: "We are going to destroy them"

Frank: "Yes we are"

Is it something that they realized only after watching the clip or is it a confidence that's been building up and fueled by their "reunion", which is symbolically represented by Frank hanging up the phone and going into Claire's room?

Answer 1

I believe that was the Underwoods expressing their newly re-enforced confidence. The video showed them as a couple when their union was probably at its strongest, before the power of the White House divided them. It recalled to them how effective their partnership was when they were all on the same wavelength (seasons 1 and 2 effectively), and now that they had finally put their differences behind them they are confident that they are now more than a match for the "prefect young couple" of the Conways.

Answer 2

Theory: At the very beginning of the video, Hannah says that she is pregnant with her daughter(note: daughter) and that she is 7 months. Given that this was Dec 31 2012, this would mean that the daughter should be roughly 4 years old.

Quite clearly, in 2016, the daughter seems to be clinging on to Hannah and drinking out of sippy cups meant for 2 year old. So does the daughter's perceptible height.

Unless this is an editorial mistake, there is more to the Conway family. Perhaps, some skeleton in the cupboards that the Underwoods smell?