I presume genealogists start te same way as scientists - look at what is known and then make an hypothesis as to the mechanism - then test that hypothesis by looking both for confirmatory evidence in that it predicts or better explains other events and negative evidence that it does not explain some points.
I started off with assumption that as name Adam was unusual and that as children were noted within the same time frame there was only the one Adam - however the burial of a child in the 'wrong' yard was a negative point. I then had a minor paradigm shift and realised that there must be two Adam Caines and suddenly all was light.

In your case the erroneous assumption being held onto is that the Ann Cain als Corlett is the widow/wife of Adam - I realised that she is considerably older than you claim and was the widow of John the Miller (his second wife) - now all names and relationships fit into place - that is what I have been trying to get you to see - your hypothesis leads to impossibilities and/or clashes with the written evidence when the children are followed up.

This of course ignores the other key disagreement in that I do not believe the Patrick son of Adam emigrated but remains buried in Ballaugh.