The basics, I believe it is from the 60s or early-70s, but it could have been from the 50s. It's about pioneers in early America and I think it had Green or Valley (or both) in the title. The cover was green, too I believe.

In the beginning a boy is out in the woods and he hears the ringing of an axe cutting down trees, so he goes and tells his father. The father then decides that the neighbors are getting too close so they decide to move out West. A lot of the story was this family traveling West.

I remember it being really similar to "Look to the Mountain."

I know this is very vague, but I couldn't think of a better place to ask. My father gave it to me to read years and years ago, and neither of us can remember the title.