It looks very likely that, like Patrick Joseph, another two of the Goodwin siblings left Ireland for America, both ending up in Providence, Rhode Island. The 'Ancestry' website has a lot of documentation to support this, and while some of the detail like dates and places of birth is occasionally awry, other detail is compelling and in the round, leaves little doubt that it is indeed them.
Firstly, James Goodwin born 29 December 1893, he sailed to New York on the Cameronia in 1914, the manifest shows him as a 20 year old single man, last residence Fivemiletown, nearest relative is his father John Goodwin, James is recorded as heading to Philadelphia to join his uncle Joseph Lynch. By the time of his declaration of intention to naturalise in 1919, he's living in Rumford, Rhode Island, although his stated birth place is correct (Co. Tyrone), his stated DOB isn't (out by 1 1/2 years), but the detail he provides on his emigration journey matches the 1914 sailing on the Cameronia - also, he calls himself James 'Arthur' Goodwin - I couldn't find any baptisms online for the children of John Goodwin and Sarah Lynch, maybe the registers are still held locally, but it might be the case that Arthur was a baptismal name. The 'FamilySearch' website has a 1921 passport application for James, together with a clear photograph. Unfortunately, the news isn't good for James, the Rhode Island Deaths and Burials collection on the 'FamilySearch' website shows that he died in his thirties in 1930 in Providence City Hospital, his parents recorded as John Goodwin and Sarah Lynch from Ireland, the informant was his wife Annie M. Goodwin and he was buried in Mount Saint Mary Cemetery, Pawtucket. I found James and Annie in the 1925 Rhode Island State Census and the 1930 US Federal Census - no children that I can see.
Secondly, Esther Elizabeth Goodwin born 4 June 1903, she emigrated and married a Hugh Walsh, like her brother James Arthur she is often mentioned with another forename, in this case Esther 'Catherine' (maybe again a batismal name), Esther died in 1987 at Pawtucket and was buried in Swan Point cemetery (the 'Findagrave' website records her under 'Esther Cathrine Goodwin Walsh', but the name on the gravestone is 'Esther E Walsh'). The cemetery record states her parents as John & Sarah (Lynch) Goodwin. In her petition to naturalise in 1927 she calls herself Esther Catherine Walsh and says she was born on 4 June 1903 (spot on!) at 'Aughangauly, Tyrone, Ireland', which is clearly meant to be Aghingowly and isn't correct (she was born in neighbouring Edergole townland), but I think she can be forgiven for that. She goes on to say that she first arrived at New York in 1922 aboard the Assyria and that she married Hugh in Providence in 1924. By the time of the 1940 US Federal Census, I can see 3 sons and 4 daughters to this couple, so every chance of living descendants today.