It may not be the one, but according to The Folk Music Index a song titled "Red Mountain Wine" is performed by:

1. Alden, Ray. Old Time Friends, Marimac 9009, Cas (1987), cut# 18
2. Kimble Family. Eight Miles Apart, Heritage (Galax) 022, LP (1979), cut# 18
3. Kimble Family. Pine Knots School Rowdies, Marimac 9037, Cas (1992), cut# 3

And on LOST & FOUND: CLASSIC BLUEGRASS (Rebel CD-1112).

~Masato