Your grandmother's version seems to be a modified version of a song I've found that's otherwise only associated with Ireland. Here's an example sung by Miss Bridget Geary of Camphire, Cappoquin, Co. Waterford in August 1906. Apparently the singer used a ballad sheet in her rendition, but I haven't located one. From Folk Song Society Journal, Vol. 3 (1907), pp. 24-25 (some linebreaks added for continuity)

FAREWELL TO THE VILLAGE

At the dawn of the morning the ship will be sailing,
That takes me away from the land of my birth,
I am forced into leaving the home I was born in,
The Garden of Eden, the fairest on earth.

It is not my wish I should part from old Erin,
Or leave that sweet cot at the foot of the hill,
’Tis nought but oppression now tears us asunder,
For the love of my country shall cling to me still.

Chorus—Farewell to the village, farewell to the green,
Where it's oftimes I danced with a blue-eyed Colleen,
My heart is nearly breaking with sorrow and pain,
For leaving the home I may ne'er see again.

The home of my fathers, his birthplace for ages,
Was torn from our grip by the governor’s hand,
My people and me were nothing but strangers,
As Irishmen are, in their own native land.

It has broken the hearts of my father and mother,
Thank God! they’re at rest in their own native clay.
My heart is nearly breaking with sorrow and pain,
For leaving the home I may ne'er see again.

Farewell to the dance on the green every evening,
Farewell to the Colleen so beauteous and bright!
Farewell to the stories we've told to each other,
While around the turf fire on a cold winter's night.

They say, in the land far across the Atlantic
It is there that the Irishman happy can be,
Where the stars and the stripes shelter every stranger,
May Ireland be soon, like it, happy and free.

Bridget Geary took the words of this song from a ballad-sheet. Mrs. Clandillon writes that she and her husband know the ballad well, but only in Irish. She does not think that either words or air have been published. She adds that Mr. Patrick O’Shea sings a version of this tune to Irish words about “John the Smith.”— L. E. B.

This tune has Æolian characteristics, but not the Æolian cadence.—R. V. W.

Otherwise, I've only found brief snippets; see link and link

A mudcat thread (click) notes that the song was published in Songs in Irish Emigrant Ballads and Songs (Robert L. Wright, 1975)