Hi
Did your paternal grandmother have any brothers whose sons had sons who you could approach for a DNA sample? If so, could be fun to test their Y DNA and see what haplogroup they turn out to be and where that haplogroup originated. DNA testing companies may well offer Father's Day sales in June. Like all genealogy, you never know what you will find!
Valerie
Yes, if you are a man and you test your Y DNA, the testing companies are quick to tell you that your ultimate male ancestor in the direct line was "Celtic", "Anglo-Saxon", "Norse" or whatever, but they don't seem so keen to predict ethnicity from an mtDNA test. I may be wrong, but I don't think that the mtDNA haplogroups are associated in the same way with particular ethnic groups.
To illustrate how confusing the whole issue is, my mtDNA haplogroup is J1c2. The ultimate J ancestress is supposed to have lived in the Middle East about 50,000 years ago, and that haplogroup is still common there, especially among the Bedouin (my distant cousins?). But the J1c2 clade or subgroup seems to have developed in Europe, and my earliest known female ancestor (mother's mother's mother etc.) was an Ulster Presbyterian in Belfast with a Scottish surname. I have quite a few matches with other J1c people whose ancestry goes back to northern Ireland, so do I count my J ancestry as "Celtic"? The problem there is that I also have matches (and have corresponded with some of them) who are Norwegian or Norwegian-American. So is there Viking ancestry there? You pays your money and you takes your choice.
Harry