Hi Avril - I guess you've already been in contact with le Cercle de Carteret? If not, then try the following link:
http://www.decarteret.org.uk/database/wc03/wc03_472.htm
Hope this helps, Cheryl.

PS: This is what I found on their site, but no marriage to Betsy de la Mare is mentioned:
Name: Thomas Alfred De Carteret; Birth: 2 Nov 1859, Sark
Father: Thomas John De Carteret (1831-); Mother: Elizabeth Le Sauvage

Spouses
1 Marie Augustine Laine
Father John Laine

Marriage 4 Jul 1885, St Michael Du Vale.Guernsey

Children
Thomas John, (1885-); Elise Maria, (1887-); John Harry Wilhiem (1891-); Thomas Henry (1899-)