Duncan Emrich printed a version in his 'American Folk Poetry' that seems close to what you want. It was recorded from the singing of Horton Barker at Chilhowie, Virginia, in 1939 for the Library of Congress:

THE TWO SISTERS

There was an old woman lived on the seashore
Bow and balance to me
There was an old woman lived on the seashore
Her number of daughters one, two, three, four
And I'll be true to my love if my love'll be true to me

There was a young man came by to see them
Bow and balance to me
There was a young man came by to see them
And the oldest one got struck on him
And I'll be true to my love if my love'll be true to me

He bought the youngest a beaver hat
And the oldest one got mad at that

'Oh, sister, oh, sister, let's walk the seashore
And see the ships as they sail o'er'

While these two sisters were walking the shore
The oldest pushed the youngest o'er

'Oh, sister, oh, sister, please lend me your hand
And you will have Willie and all of his land'

'I never, I never will lend you a hand
But I'll have Willie and all of his land'

Sometime she sank and sometime she swam
Until she came to the old mill dam

The miller got his fishing hook
And fished the maiden out of the brook

'Oh, miller, oh, miller, here's five gold rings
To push the maiden in again'

The miller received those five gold rings
Bow and balance to me
The miller received those five gold rings
And pushed the maiden in again
And I'll be true to my love if my love'll be true to me

The miller was hung at his mill gate
Bow and balance to me
The miller was hung at his mill gate
For drowning little sister Kate
And I'll be true to my love if my love'll be true to me

--Stewie