It's a great story. It seems that John was a great globe trotter, first to Australia, back and then to the States, And then backwards and forwards.

Just a small problem. The emigration on the City of Antwerp 1872.....  Seems that the names and ages don't quite match up. For example: John is recorded as being 20 years of age, that would make him born in 1852, Bridget (susposedly his daughter) is recorded as being 7. So John was 13 when she was born, and had already got married and gone to Australia.

Eliza is recorded as a spinster (not married) and 18 years of age. So she was 11 when Bridget was born..........

If we accept that he sometimes used the name Flahy, then Ancestry has a marriage to Eliza Fitzgerald in Ballyvaughan (not Carron) on the 30 April 1864 (not 3 April 1864). The Carron version does not show up on https://registers.nli.ie although that may not be complete.

I agree he ages not match up, but that is a common problem even on census. They didn’t pay attention to such things and usually didn’t even know their birthdates. I am highly confident this record is John and his family. After arriving, they went to Providence, Rhode Island. The young child Patrick became ill with spinal meningitis and died. I obtained his death record. They remain in Providence until Mary Ellen is born and then travel back to County Clare where they lived in the Burren until the late 1880's and had several more children. I have documented the births of all the remaining children. The births I have not been able to document are his oldest two daughters who said they were born in Australia. I have DNA connected to some Fitzgerald's there and am working on a theory based on some ship records that after their marriage in April 1864, Eliza went first to Australia with her brother. John followed a couple months later. I believe if the record is him that he arrived in Dec 1864 and Bridget is born March 1865.  Bridget always claimed her birth date as March 17, 1865. Catherine the next child and my great grandmother was said to have been born in 1866 on Australian waters, I believe on their return to Ireland. From that point I can trace them living in the Burren, John as a herd and Thomas and Patrick are born and baptized in the Carron chapel. I have these records. They then go (on the City of Antwerp) along with an older Bridget Lahiff (I believe his mother) and the children Bridget, Catherine Kate, Thomas and Patrick. As stated above, soon after their arrival they go to Providence and Patrick dies.  Mary Ellen is born in Providence Rhode Island (documented and and they return to Ireland. Why, I do not know but their remaining children are all born and baptized in Carran church. They return to America and live in Newport. I have seen their house and visited their graves there.  I agree with you that such travel was unusual, and I do not envy their lives but they were hearty and strong and their children grew up to do some amazing things  

The actual marriage date was the 30 of April not 3. That was a typo on my part. 
I have their marriage record which states they were married in the Carron Chapel. The civil record was done in Ballyvaughan. Carron was close to where the Lahiff's and Fitzgerald families lived as herders. 

I now have birth records for Bridget and Catherine, so all family records are complete.  I was given a tip and followed it. Found John and Eliza arriving in Wellington , NZ one year after their marriage. Found a diary of the ship Berar and was able to connect the birth of the Bridget their first child on board the ship Berar. She was also baptized. The author of the diary recorded both. The Diary of the Ship Berar is available at Wellington library in NZ.  While in Wellington, their second child Catherine was born. Found her birth and baptism record there. Shortly after her baptism, they returned to Ireland.