YouTube video of this:

http://www.youtube.com/watch?v=KGa-lfz5Vbw

I believe you are right. It's a mountain dulcimer and a guitar. The dulcimer sounds funny - loose, somehow. Maybe it's a zither.

I played the line 'make my bed, Mommy do,' on my keyboard, and it has many black notes. In fact, it has every black note there is, plus an F. That would not be typical for a dulcimer.

I don't know what key it is.