In the Harry Potter books, we never get to know who Voldemort's grandmother is on the Gaunt side; and in the memory in the 6th book, we only see Marvolo, Merope, and Morfin Gaunt. Does anyone know anything about Marvolo's wife and why we never saw her?
Dumbledore himself says in Half-Blood Prince that Gaunts had a tradition of marrying in their own family.
"Voldemort's grandfather, yes," said Dumbledore. "Marvolo, his son, Morfin, and his daughter, Merope, were the last of the Gaunts, a very ancient Wizarding family noted for a vein of instability and violence that flourished through the generations due to their habit of marrying their own cousins.
~Half-Blood Prince, Ch 10: The hour of Gaunt
On the website of Harry Potter Wiki (in the section of Marvolo Gaunt) his wife's name is not mentioned even in the Gaunt family tree.
It was never mentioned about Marvolo's wife or how she was absent from the Gaunt shack (arguably most likely dying sometime before the arrest of her husband and son), but it could be surmised that given his terrible treatment of Merope, Marvolo also made for a horrible husband. (Link: http://harrypotter.wikia.com/wiki/Marvolo_Gaunt)
Another link verifies the claim of Gaunts marrying into their family:
The Gaunts are an ancient, in-bred, Pure-blood Wizarding family, direct descendants of Salazar Slytherin.
So I guess its safe to assume that she was most definitely a family member, a cousin most likely.