Thanks for that, it clears things up for me! Richard and Elizabeth's daughter (my Great Grandmother) Elizabeth Jane Cavendish married Walter Corlett Cleator on 1st June 1886 at St. George's, Braddan (I have the certificate). They left for Bolton, Lancashire in c. 1896 and Walter deserted the family in c. 1902 to go to the USA, where he died. Elizabeth Jane died in Bolton and was buried on 5th Feb. 1925 in Deane Churchyard, Bolton.
Regarding Moore connections, you may not be aware that the 1871 and 1881 census entries for Richard and Elizabeth Cavendish show a Robert S. Moore as lodger, aged 5 and 15. The 1881 census also shows Annie Cavendish, Granddaughter present. As Thomas Richard appears to be Richard and Elizabeth's only son, this would make her a daughter of your Great Grandparents.
Regards
Mike