Hello Martin,
Thanks for the update. So Susan registered the birth, and had probably invented the father's name for her illegitimate children as we were unable to find him elsewhere. More importantly the children must have been fully accepted as being Fynney or their uncle wouldn't have made the English settlement for them and Susan. It is also notable that he referred to her as "Mrs.Susan Fynney" when there was no sign of a marriage - she must have been a convincing person!
The children's surname appeared to have always been recorded as Dixon in the IOM but Fynney in England.
Did you also either order a photocopy of the bapt or look up the LDS film entry for Augustus Fredic Synney Dixon on 2 Oct.1870 Saint Barnabas, Douglas? Just in case it gives more information? [LDS film no.0106187]
The other two children were bapt at Saint George, Douglas [LDS film no.0106186] - all these entries could give more details.
Sue