THANK YOU so much for your data. You are quite right about the parish records.A wonderful lady in Sweden has tracked down much of the family for me.The glitches are in the emigrants, some of whom disappear and reappear in a manner not consistent with the oral history: nameless "cousins"perhaps lived for a time in both Canada and the USA,in the same area as other members of the family, generally between census years. Tracking them is a bit like herding cats.
And about the illegitimate children: both the Church and the community frowned on such, so I was surprised that the children were raised at the grandfather's home.In researching the time period, I came across an article that might help to explain it. (Forgive me for working from memory here) It was a requirement that a person be able read and write before being married.Perhaps one of them had a problem with this, which was either solved or they eventually were given permission to marry anyway?