I finally talked to my friend who first played this song for me. Between the two of us, and using the above posts to jog our memories, I've come up with these lyrics, which are pretty much dead on, as far as the version he played for me goes.
He said the CD was some compilation of Celtic women's music, but that it was NOT by Nancy McAlion or The Mollys.

 ON WE GO

 There was an old woman and there was an old man,
 Who laid upon the high road.
 He once said, as a chucky for his pay,
 That she was her mother's darlin'-O.
 
Chorus:
On we go, on we go
Can you recall that we'd be married-O?
On we go, on we go,
Would ye leave me pregnant, see me die alone?
Come a little closer to me, darlin'-O.
 
"Come with me, you silly old man,
Cozy as a codfish-O.
I've never seen anyone hard as you,
At least not after breakfast-O.

 Chorus:

 She took the old man by the hand
 And led him across a moonlit night.
 She took him to the public house
 And filled 'im full o' whiskey-O!

 Chorus: 

 On the way back home from town,
 Oh, woe, my darling-O!
 She pushed him in the water and held him down, [shouting:]
 "Can you recall that we'd be married-O?"

 Chorus: 
 On we go, on we go
 Can you recall that we'd be married'-O?
 On we go, on we go,
 Would ye leave me pregnant, see me die alone?
 Come a little closer to me, darlin'-O.
 [Softer] Come a little closer to me, darlin'-O.
 [Whispered very pointedly] Come a little closer to me, darlin'-O!.

Personally, I think this version is more interesting, and the woman has more justification for her actions than is apparent in the Mollys' version. But that's folk music, innit?

Genie