I cam across yet another version of this story. I found it on an album titled Here's to the Men by the Merry Maids of Windsor, and then I found the lyrics at one of "those" Websites, http://lyrics.wikia.com/The_Merry_Wives_Of_Windsor:All_The_Lads_In_Town
I've corrected the lyrics as I hear them on the recording. I don't know the name of the songwriter.

ALL THE LADS IN TOWN
(songwriter?)

Johnny is a handsome lad
And asked me for to wed.
And I would marry Johnny
But me father up and said,
"I am sorry to tell you, daughter,
What your mother never knew,
But Johnny is a son of mine
And so is kin to you."

The boy that I will marry will be handsome, strong, and tall,
And he will sing my praises and be at my beck and call.
The boy that I will marry will keep me satiated,
And every night in bed I'll pray that we are not related.

William is a handsome lad
And so is Pat O'Brian.
So too is Mickey Grady
And his younger brother Ryan.
But father was a busy man.
His seed so far did spread.
He told me they're my brothers all.
So safe my maidenhead.

The boy that I will marry will be handsome, strong, and tall,
And he will sing my praises and be at my beck and call.
The boy that I will marry will keep me satiated,
And every night in bed I'll pray that we are not related.

Ye never saw a lass so sad
And sorry as I was.
The lads in town were all my kin
And me father was the cause.
If I should die a single maid
For that adulterer's sport,
I think I'll go to mother for
His wanderings to report.

"Now, daughter, didn't I teach you
To forgive and to forget?
Himself he sowed his wild oats,
But that you needn't fret.
Your father may be father
To all the lads but still,
He's not the one that sired you
So marry who you will."

The boy that I will marry will be handsome, strong, and tall,
And he will sing my praises and be at my beck and call.
And since my mother twiddled with a sailor come from sea,
I'll find myself a handsome lad who'll not be kin to me.

The boy that I will marry will be handsome, strong, and tall,
And he will sing my praises and be at my beck and call.
The boy that I will marry will keep me satiated,
And every night in bed I'll pray that we are not related.