Hi Simone,
In case you haven't received an answer to your 2007 query, I think I can help.
I also have looked for the marriage of Thomas Peter DeCarteret and Anne DesCaudeville in the Sark marriage records (and the Guernsey records) and haven't found it. They are both in the 1881 Sark census as unmarried and in the 1891 census as married to each other. Their first child was born on Sark in 1885. Perhaps they were married on Jersey between 1881 and 1885.
Anne DesCaudeville and Anne Cook are the same person and the marriage of Thomas and Anne is the only marriage for both of them. At this time in the Channel Islands you see the surname as DesCaudeville dit Le Cook (called Le Cook) or DesCaudeville dit Le Cocq and some dropped the DesCaudeville part and just went by Le Cocq or Cook as time went on.
The reason why the two oldest children have the DesCaudeville surname is that they are illegitimate and were born before 1881 so they have their mother's name (although Stephen is listed as DeCarteret in the 1891 census). Their baptism records don't list a father.
Anne's birth date is Aug 13, 1859 and she was baptised Sept 7, 1859. Her parents are James DesCaudeville of Sark and Jeanne Rouget from St Peter, Jersey.
Hope this information has helped.