This would be a obvious case for DNA.
From what I can see. James of the 1901 census in Tullow was a cooper and there is indeed a cooper called James Hopkins, married, from Tullow, father Nicholas, estimated year of birth 1880, going to Rochester on the Teutonic in 1908.
I don't see James on the 1911 census in Ireland. Was he staying elsewhere?
'A' James, father of Lucille, married (about 1916 or 17) to 'Annie' appears on the 1930 Federal census in Chicago. He has five children, including Lucille. This man does not have a trade, or at least is not working as a cooper, rather peddling vegetables.
The same James appears to be in the 1920 Federal census, (Chicago) with Annie and three sons. He works as a labourer.
The 1920 James gives his naturalisation as 1917.
A James Hopkins is naturalised and his documents list him as from 'Carlow'.
His date of birth of the naturalisation documents is given as 27 September 1879.
In the petition (1918) he lists himself as not married.
In the declaration (1921) he lists himself as married to Anna and with a number of children, including Lucille.
Most interesting. I suppose the thing to look for would be a marriage cert. in the US for this James Hopkins and his Anna - to rule things in or out. The main thing I would find unusual is that a skilled man like a cooper took work as a labourer (if indeed they are the same person).
**edit A search for one of the sons, Terence Francis Hopkins, shows a mother's name as Anne Dunn.
There is a marriage in Cook County Illinois between a James Hopkins and an Annie Dunne on 3 Sep 1918. I guess that would be the cert to chase up to see if parents' names are mentioned.