Rell,
Here’s a possible death for a John Poole who was a labourer and lived in Tullyveery townland, which includes the village of Shrigley. Could well be your John & Alexander’s father.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1891/06075/4732384.pdf
Informant was his daughter Marianne Heaney (Haney) also of Tullyveery. This looks to be her marriage in 1878 in Killyleagh Presbyterian church;
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1878/11087/8057798.pdf
Tradition was to marry in the bride’s church so that suggests the Poole family were Presbyterian and that would be the relevant set of records to research if trying to take the family back a bit. The Killyleagh Presbyterian baptism & marriage records start in 1693 but there’s a gap between 1757 and 1835. Copy held in PRONI in Belfast. Presbyterians generally didn’t keep burial records. And labourers families are unlikely to have a gravestone.
Can’t see a death for Ann Poole but death registration only started in 1864 so if she died before that, there is no record. I looked at the statutory births 1864 onwards and did not find any children to John & Ann so suspect she may have died. There was a Mary Ann Poole death in 1868 aged 48. That year is still pay to view so can’t give you the details but you can pay to view it on the GRONI site if you want:
https://geni.nidirect.gov.uk
Here’s the family in 1901, by which time they are Church of Ireland (indicating Joseph was probably that denomination). Mary Anne was born in Co Down c1862:
http://www.census.nationalarchives.ie/pages/1901/Down/Killyleagh/Shrigley_Village/1231020/
Doffer is a process in the linen making industry. Note David Poole lodging with the family. Presumably another brother.
Joseph Heaney in 1911:
http://www.census.nationalarchives.ie/pages/1911/Down/Killyleagh/Shrigley_Village/240376/
Mary Anne died in 1909:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1909/05454/4526457.pdf
Odd that Alexander was apparently born in Antrim. If accurate, presumably the family moved for some reason. Finding his baptism without any idea of where in the county it took place will be challenging. But I'd also check Killyleagh records in case that's where he was born. Can’t see a marriage for his parents so assume they married before April 1845 which is when marriage registration began.
