The Roches would be a good educated guess, but I don't think it's them.
I've seen the Roches in concert, and their repetoire is (at least in 1995 when I saw them) mainly a capella folk music (vocals with no instruments), without any really big country influence. So I'm taking a stab in the dark, and thinking this could either be the Judds or members of the Carter family. June Carter was married to Johnny Cash, so the country influence would be much greater. plus the young daughter playing the bass bears a remarkable resemblance to June's daughter Carlene. I had a band earler this year who opened up for her. Her birthday was in February-we played on her birthday- and she told the audience she turned 52- and she has four kids and two grandkids already. And for a grandmother, she looks and sings incredible!
Given this clip was from sometime in the mid-to-late 70's it would make sense.
Somewhere on youtube is a clip of these ladies singing "Keep On the Sunny Side", which has been a country staple for a long time.
So that's my theory.