Philip, where you write Jane, as in "...Jane he gets wrong, for he says that she married first Peter Chandler, and secondly a Killip, with a child Alfred, who died (presumably in infancy)" do you mean Isabella Joughin/Kermode/Killip?
Or Isabella's sister Jane Joughin? Or Isabella's daughter Jane Kermode aged 9 in 1861?

I felt sorry for Jane Joughin, being alone in charge of her sister's 3 young children when she was only 21, in 1861.

I couldn't see a burial for James Killip before 1861, although there may be a M.I. Or he could have remarried and was living elsewhere, having left Alfred with his parents. In 1871 Alfred C Killip aged 11 was living in Douglas [Ballacrink] with his grandparents James Killip 65 House Joiner, Ann Killip 66, and their granddaur Sophia J Killip 13. [? Sophia Jane bapt 6 June 1858 Saint Barnabas, Douglas, Father: John KILLIP, Mother: Eliza]

In 1881 Alfred Killip aged 22, b.Onchan, residence Onchan, was a fisherman on the 'Bonnie Lass'. Ancestry says "Fisherman at Kinsale Mackerel Fishing".

Judging by the details in the 1861 census I think James Killip was probably bapt 13 June 1824 Braddan, the son of James Killip and Ann Christian. There was another James Killip in censuses, the same age, but he was b.German and with his [different] parents in 1861.

If I change the subject heading one of the Killip researchers may help.

Sue