From the First Ladies site
Birth:
Place: Chicago, Illinois
Date: 1947, October 26
Father:
Hugh Ellsworth Rodham, born 1911, April 2, Scranton, Pennsylvania, graduate of Pennsylvania State University, small textile supply owner; died, 1993, April 7 in Little Rock, Arkansas
Mother:
Dorothy Emma Howell Rodham, born 1919, Chicago, Illinois; married to Hugh Rodham, 1942
Ancestry:
Welsh, French, Scottish, Native American, English; Hillary Clinton's paternal grandfather Hugh Rodham was born in 1879 in Northumberland, Wales and immigrated to Pennsylvania to work at the Scranton Lace Company. Her maternal great-grandparents, the Howells, were immigrants from England and settled in California. Her maternal grandmother, Della Murray migrated from Canada to Illinois and married secondly to Max Rosenberg who was born in Russia in 1901.
Education:
Eugene Field Elementary School, Park Ridge, Illinois, 1953-1957; Ralph Waldo Emerson Middle School, Park Ridge, Illinois, 1957-1961; Maine Township High School, East and South, Park Ridge, 1961-1965,
What's missing is wether her grandfather, either one of them, owned a cottage in Pennsylvania while she was a little girl (which I'd define as up to 12 years old, making it around 1959 at the latest..
Here is an article indicating that she and her family did indeed spend much time in the Poconos of PA when she was a little girl
It mentions that cabin/cottage near Lake Winola. (The link is not to the original source, but I checked there, and could not find it, but there was a dead link from the page linked above to the original source site. They probably moved the article, and since the article goes back to Sept of 2007, it's a bit hard to find, and there would be a fee to access it on the original site (The Morning Call of Allentown PA) However it seems to be based in part on information provided by Clinton herself, so the date becomes important. The article linked was posted on the Chicago Tribune site in September of 2007
The article says the "cottage" still belongs to the Rodham family.
Thus, her story is quite possibly true, although the shooting part can't be verified yet by an independent source, and is only mentioned in the "headline at the linked site, but not in the original headline, which was "Summers with Hillary". The site above has a video of Her Heinousness as a little girl, littler than the gun shooter I'm sure, and the audio has Hillary saying she learned to shoot a gun there on Lake Winona.
Northumberland is not in Wales. It is a county in the north of England.