The "Betty" in that song was Elizabeth Bannard with whom Paul had a romantic attachment. At some stage she had gone away, maybe overseas, and Paul wrote the song as part of his attempt to induce her to return.
They married eventually and as far as I know they still are together.
"C'mon Betty Home" was never recorded by PP&M.
I met Peter Yarrow at a press conference in 1968 and I mentioned that song to him. He immediately started to sing it loudly. Paul was at the other side of the room being interviewed separately. He immediately spun around and asked "Who mentioned that?". Peter pointed to me and said "He did". Paul was blushing from one side of his face to the other. I have never forgotten it.
: Written by Noel ("Paul") Stookey of PP&M.