I had a look at the 1878 marriage. As you say, William Todd – farmer – was dead in 1878. His wife was named as Eliza Hampton and was alive. (William junior should have known his mother’s forename and so it’s presumably accurate). I had a look for a death for her 1878 – 1901 but did not find one in Armagh, nor was there anyone alive in Armagh in the 1901 census who might be that lady.
I did find a Mary Jane Todd from Teagy who died in 1879 aged 80 and whose husband appears to have been William Todd:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
William of Teagy died in 187:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1877/020533/7205351.pdf
William of Richmount died in 1873. His wife was Mary Jane too:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
If William Todd was a farmer and alive around 1830 he ought to appear in the tithe applotment records for Co. Armagh. (The tithes were a land tax so most farmers were listed). I found 7 farmers named William Todd in Co Armagh at that time (2 were in the same townland – Drummond More - and were probably father & son):
Todd, William-- Townland : Clanamola Year : 1828-Drumcree-Armagh
Todd, William-- Townland : Richmond Year : 1828-Drumcree-Armagh
Todd, William-- Townland : Roughan Year : 1828-Drumcree-Armagh
Todd, William-- Townland : Tumblekenny Year : 1828-Drumcree-Armagh
Todd, William-- Townland: Drummond More Year: 1832-Grange-Armagh
Todd, William-Townland: Teaguy Year: 1834-Tartaraghan-Armagh
Todd, William, Jr.-- Townland: Drummond More Year: 1832-Grange-Armagh
I looked at the 1901 census of Armagh. There were about 115 Todds. Most were Church of Ireland (ie Anglican) with a couple of Methodists, Presbyterians and RC. Methodists in Ireland didn’t perform their own marriages till the late 1830s and even then they were few and far between so most would have married in the Church of Ireland. So Church of Ireland is probably the most likely denomination for the children’s baptism and perhaps the marriage too.
Statutory marriage registration began in Ireland in 1845 (save for RC marriages which start in 1864). William & Eliza evidently married sometime before 1839 so you won’t find a statutory marriage certificate for them. You might find their marriage in church records but they probably aren’t on-line. There are copies in PRONI (the public record office) in Belfast. You could get a researcher to go through the records for the 3 parishes that there were Wm Todds in in the 1830s ie Drumcree, Grange & Tartaraghan, searching for William’s baptism and his parents marriage. That’s probably the only way of locating them in Armagh.
Drumcree’s records start in 1788, Grange 1780 and Tartaraghan in 1825. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
Your comments about William’s “inconsistency of conduct” in the Methodist chapel suggests he may not have been all that enthusiastic about religion and remarrying in church. The 1878 marriage is slightly unusual and interesting because it was by habit & repute. In other words the couple were never married by a Minister, a Civil Registrar or any other authorised official (Scotland didn’t have civil registrars till 1940). They just lived together, and then eventually used a uniquely Scottish procedure whereby a couple could appear before a Sheriff[1], with at least 2 witnesses, to confirm they had been living as man and wife for a significant period of time. If the Sheriff was satisfied – as he evidently was in this case – then he ruled that their relationship could be regarded as a valid marriage in Scots law, and if they wanted, the marriage would be recorded formally in official records. (Slightly like what folk today might call a common law marriage though often there is no legal meaning to that term. But in Scotland until 1940 you could lawfully be regarded as married in that way). And this was one of those cases. See:
http://www.gla.ac.uk/schools/socialpolitical/research/economicsocialhistory/historymedicine/scottishwayofbirthanddeath/marriage/
Elwyn
[1] A Sheriff is a lower tier court judge who deals with criminal and civil cases