It's in the database. Just enter [old home place]in the blue search box. Mitch Jayne of the Dillards wrote this. It was on the very first Dillards album in 1963, and is available on their compilation CD, There Is A Time, available from Vanguard.

When you get to the lyrics page, just go up to the top of the page and click on the link to CDNow. That will call up quite a number of recorded versions, including, of course, The Dillards! Clicking on There Is A Time will take you to sound clips of all the songs. The clip for Old Home Place even includes the plow in the field phrase that you mention.

Looking at the available recordings, I am guessing that some of them are of a different song. Anyway, I have yet to hear a better version than that of The Dillards, though that of J D Crowe is quite satisfactory, too.