Just a comment on Richard Palmer, and an early second marriage. It was by no means unusual for marriages to take place between by today's standards very young teenagers, the legal age for a girl was 12 until 1929; also there was a very heavy mortality amongst women through death in and shortly after childbirth, so remarriage very quickly was the norm, specially if the child had survived, or if there were other children to the marriage. I believe it would be worthwhile looking at this Richard again in this light, i.e.seeing whether there is a death of a Palmer wife shortly before the re marriage, and/or whether there is a record of any baptisms/ burials of children.
Just re-read your reply, had a senior moment, many of the above points had either been covered or are irelevant in the situation, however, the generalities still apply.