Okay, I did a quick look-up on teanglann.ie, and they show two words for great-grandfather (neither of which was my guess)....
1. Garathair
2. Sin-seanathair
Trying to look up"great-grand-daughter, I found the following:
Iarua (iníne) is great-grand-daughter
Iarua (mic) is great-grandson (for some weird reason, grand-daughter is hyphenated but grandson is not....)
Iarua is matched with iaró, which means "later descendant" and apparently requires the addition of a genetive designator for son or daughter. No example sentences were given, but I presume you would use either "iníne" or "mic" with "iarua" to indicate the gender of the descendant.
Iaró is an interesting term, as it means "later descendant" but does not seem to take the gender identifiers, or at least they are not shown. It does have a plural form, iaróí, and a dependent plural form "iaróibh" which is also sometimes used as the nominative plural; not sure how to differentiate when which is used.....
So I guess the question would be...do the Irish bother, as Gaeilge, to count the generations back, or do they just say "distant relative" with the appropriate term?
Interesting, if confusing, stuff!!!
Dale