"Ainneoin go mba i Meiriceá a rugadh í, tugadh go hÉirinn í in aois a trí mblian i ngeall ar bhás a máthar, agus abail a seanmháthair-Neile Thaidhg-i leathbhaile thiar Sheana Choille a tógadh í, go ndeachaigh sí ar ais arís go Meiriceá ar sharú an scóir." Cén míniú a bhaintear as "in aois a trí mblian" agus "ar sharú an scóir."? I'm assuming that "mblian" is a typo of "mbliana", but why is it eclipsed?

ar sharú an scóir - on exceeding the score (twenty)

Isn't it "in aois na trí mblian"? I believe mblian is a connacht variant of bliana, but I wouldn't swear to it. Has Ó Siadhail anything to say on the matter?

Nope. It's written the way I wrote it. Maybe it's a typo, but I still don't get it. O'Siadhail: "na trí bliana". Maybe "mblian" is a typo too.

"in aois a trí mblian" means "at the age of three", but I presume you got that.

I'm reluctant to be dogmatic about anything in Ó Cadhain's works being a typo. Unfortunately, he's not around to tell us.

May I make a wild guess?
Maybe "in aois" takes the genitive.
"Tri bliana" is a plural.
So, "in aois na tri mblian" could be translated literally as= "in the age OF three years" (a genitive plural requiring the noun bliana to be eclipsed. I really don't know why there is no "a" on the end of "blian".
O Donaill's dictionary has the following entry:-
Nominative singular - Bliain
Genitive singular - Bliana
Nominative plural - Blianta

but does not give The Genitive plural.

In the same entry the phrase "Anonn i mblianta" is given for "on in years" but I suspect I'm getting mixed up here somewhere. Can anyone unravel this for me, Please?

Nominative:
an bhliain
na blianta

Posessive:
na bliana
na mblianta

"i mbliana" is an idiom that means "this year":

Have you swam at all this year?
An raibh tú ag snámh ar chor ar bith i mbliana?

"Anonn i mblianta", well "back and forth" = "anonn is anall".

I found the following under aois in Dineen
"bhís in aois do thrí mbliadhan"

So it looks like the "a" in "in aois a trí mblian" means "her".

There is still some grammatical wierdness goind on, but perhaps the use of the possesive pronoun will trigger something in those with a deeper mastery of the finer points of grammar.

I have a strong feeling that we are getting a cascade of subordinate clause and genetive.

My dictionary gives "bliadhan" as an variant genetive plural. Maybe TSJ is right.

bliadhan is simply the pre reform spelling of bliain.