David,
Here’s Alexander’s birth cert. he was born in Largymore outside Lisburn:
https://civilrecords.irishgenealogy.ie/churchrecords/images/cert_amends/cert_1870/2223912a.pdf
Parents marriage in 1869:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1869/11408/8189370.pdf
They had son William born 19.2.1872 in Largymore. The family appear to have moved to Ayrshire after that. Cecilia was born in Dalrymple in 1874. Samuel & Eliza both die din Ayrshire (1924 & 1913 respectively). It doesn’t look as though anyone remained in Ireland save for Samuel’s parents and any siblings he may have had.
At least 1 tree on Ancestry (The Wilson family) has this Rosann Hawthorn as Samuel’s mother. She died in 1872 aged 60.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1872/020750/7279675.pdf
However that same tree has Samuel’s father William dying in Lisburn in 1896. But if Rosann was his wife, she was a widow in 1872, and so he pre-deceased her. That Ancestry tree does not therefore appear to be completely accurate.
Same tree on Ancestry lists 3 possible brothers for Samuel. Thomas? b 1861, Robert 1862 – 1936 and John (no dates). Robert also appears to have headed for Scotland. He died in Glasgow in 1936. No information on the other two brothers.