Sharonl,
The Timothy Irvins who died in 1867 was a cabinet maker, not a labourer, so I don’t think it’s your family at all. I remain pretty sure your Timothy died pre 1864. I think as you say, someone just guessed that death without checking anything. Your information that Timothy died just before emigrating would perhaps point to a death around 1843 to me. If he was Presbyterian and a labourer, there won’t be a church record of his burial and he almost certainly wouldn’t have been able to afford a gravestone.
It’s unusual for elderly people to emigrate. They usually prefer to stay where they are, with familiar surroundings. They rarely fully settle in the new land, if they do go. If Timothy had been thinking of emigrating, it’s more likely that he’d have done that when he was still of working age. (The most popular age for migrating was/is your 20s. But folk aged 40 often went. Folk aged 70 only did it in extremis). If Andrew was thinking of emigrating in the early 1840s, then maybe his father was part of that plan.
There are a lot of poorly researched trees on Ancestry, and a lot of care is needed with them. They are a useful starting off point but a lot of the early information is often wrong. Something that I suspect folk don’t understand fully is that most of the pre 1901 Irish censuses are lost, save for some fragments, whereas the Scottish (and English) censuses for 1841 – 1891 all still exist. Most Scottish Presbyterian baptism records are on-line. Most Irish Presbyterian baptism records are not. When you get a common Scottish name like William Irvine, Ancestry automatically searches the Scottish censuses and baptisms and throws up possible matches there. William Irvine in Eastwood could well be a typical example. So people seize on this and think it’s their family, and into the tree it happily goes. Apparently untroubled in this case by the fact that the wife’s name is completely wrong.
You mention the family not showing up in censuses. Well the simple explanation is that they don’t exist in Ireland, save for a few fragments. They were destroyed, some as a result of the 1922 fire and some were pulped during a paper shortage. There were censuses in 1821, 1831 and 1841 which would have included your family but they are all largely destroyed now, certainly for the area where your family lived. That’s why you can’t find them in any census.
Regarding Timothy marrying in the Church of Ireland, that’s perfectly possible. Tradition was to marry in the bride’s church, after which she’d normally attend her husband’s. So if Timothy’s wife was Church of Ireland that’s where they’d have married. It’s probably also where they would have married if she’d been Catholic. The RC church would not marry mixed denomination couples then (indeed they are not very keen on it now) but the Church of Ireland would, so that’s where many mixed denomination couples went. (After 1845 they also had the option of a Register Office which William & Margaret O’Hara chose, suggesting to me she was RC). Several of the trees also have Timothy marrying a Margaret O’Hara too. Bit of a coincidence? But might be correct. Probably not though.
There was a slight question mark over the validity of Presbyterian marriages pre 1845 (when the law changed and formally validated them) particularly if they were of mixed denomination. People with land sometimes used the Church of Ireland because they were worried about inheritance issues if the marriage was ruled invalid. However the average labourer had no such concerns and the record books are full of Presbyterian marriages back to the 1600s. So most Presbyterians would marry in their own church. But as I say if the bride was RC or Church of Ireland, then they may have married in the Church of Ireland. But their children would normally be baptised in the husband’s church.
It is odd that only Andrew shows up in Ballyeaston’s baptism records. Their records only start in 1814 so if any were before that then that would be one explanation. But the family moving and using a different church would be another. Braetown is near Glenwherry Presbyterian church. It has no baptisms before 1845 (records either lost or never kept). So they might have been baptised there and if so you’ll never know.
Rashee & Ballycor are not the same place. They are separate parishes but they are adjacent so it wouldn’t be unusual for a labourer to be living in one and then later appear in the other. Map attached:
https://www.johngrenham.com/browse/county_civil.php?county=Antrim
Presbyterians in Ireland don’t actually use the parish system. Which church you attended was a matter of personal choice or whim, and not always the closest to where you lived. If you want to check all the Presbyterian baptism records in that general area you can see what records exist, and what years they cover in the PRONI guide. The records themselves are not on-line and so you need to go to PRONI to look them up (or get a researcher to do that for you). This link explains what records exist, parish by parish:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
Labourers moved about to follow the available work. They tended to rent a cottage from a farmer. Rent could be paid in cash but was often paid by an agreed number of days work on the farm each year, after which the labourer was free to take any other work that was available, eg on other farms or on government contracts eg road building. In the winter months they often wove on hand loom weaving machines similar to those still used in the Outer Hebrides to make Harris Tweed. The main product in Ireland in the 1840s would have been linen but they did also weave calico, wool, and other products. Changing agricultural practices including some mechanisation were starting the reduce the need for labourers on farms and water powered mills made linen faster and to a better standard than most home weaving, so that was rendering home weaving less economic. A population explosion and various attacks of potato blight all influenced the decision to emigrate.
Margaret could well be the daughter who stayed in Ireland. There also remains the question of what happened to William Irvine and Margaret O’Hara, after they married in 1854? I reckon he’s part of the family too. Timothy is a very rare name and William was living pretty close to Ballynashee. I looked for statutory births for that couple 1864 onwards but didn’t see any, suggesting they had left Ireland (or had no children).
Emigrants in the 1840s could have sailed from Belfast but there were also sailings from places like Larne and Londonderry. And a lot sailed from Liverpool. The agents often threw in the short journey to Liverpool as part of the package. Liverpool then was acting as a clearing house for emigrants from most of Europe and so had many more departures to North America than there were directly from Ireland.
I have attached an advert from the Belfast Commercial Chronicle 1828 for emigrants to obtain land in Canada and also a letter from 1847 summarising that summers likely emigrant traffic. Also a page from the Northern Whig 21.3.1843 (a Belfast paper) with adverts for sailings to Canada from Belfast & Liverpool. Perhaps gives a flavour of the times.