My mother's parents were both born in Ireland; grandpa is from Rathkeal, Limerick and grandma is from around Lurgan, Antrim. Due to some "insubordination" from my great-great grandfather (directed at the British Army), my grandmother's family was forced to flee to Scotland. It's a funny story, actually...he was a train conductor, and one day was assigned to transport a company of British regulars from the Midlands to somewhere in Sligo. After a hurried conversation with the other employees, they decided to waylay the Brits. Somehow, he convinced the Officer Commanding that their destination was "just over that hill" when he dropped them off. Well, he stopped at a rural station and directed the soldiers towards naught but a swath of bogland.
He gathered his immediate family and left for Scotland about a day later, and apparently the police were searching for him after he departed. Obviously it was safe to return a generation later, and my grandmother was raised in Edinburgh and Ireland. After her education at the University of Edinburgh, she left for the U.S. My dad's side is more mixed. His grandmother was 100& Irish, his grandfather 100% Polish. Through some research, I've learned that the Polish folks were actually transplanted Lithuanians. My dad's mother on that side has a very mixed heritage: French, some Dutch, something else as well IIRC. One thing I do know: If my great-great grandparents hadn't changed their name from "Pavlovski" to a shortened version, I'd be getting a lot of dog jokes.