How easy/difficult is it to emigrate to America?

[ruadh]

OK. We’ll take this clause by clause.

if you were born in an ineligible country

Which you were - you were born in Britain

but neither of your parents was born there

Your mother wasn’t born there - she was born in Ireland. Was your father born there (Britain)? If so, sorry, you’re not eligible. If however he wasn’t born in Britain, go onto the next clause:

or [neither of your parents] resided there at the time of your birth

Were your parents living in Britain at the time you were born? If so, you aren’t eligible.

This exception to the nativity rule is for people who have no connection to a country other than that their mother happened to be physically present in it at the time of their birth. It’s for people whose parents were essentially just passing through the country when they were born. Obviously, this is a really, really small number of people - and it’s intended to be. The State Department likes to keep things easy.

[Lobelia_Overhill]

OK so does that mean I can’t emigrate, or just that I don’t qualify for a Green Card?

[ruadh]

It just means that you don’t qualify for the Diversity Visa. The other routes to US residence (marriage or employment based) would still be open to you if you could find a sponsor.