It's been a while since your post so perhaps you've found her. But if not I have a possibility for you -
There was an Ane Marie Gydesen born on Sept 20 1866 in Randbol parish, Vejle Amt. Her parents were Markus Gydesen and Kristine Nielsen.
Markus Gydesen was born on Dec 23rd 1839 in Norup parish, Veile. His parents were Gyde Thomsen and Ane Marie Jensdatter.
Kristine Nielsen was born in Vorbasse parish, Ribe Amt on July 19 1842. her parents were Niels Christensen and Else Andersdatter.
At the time of the 1880 census they were living in Sonder Omme parish and the family consisted of
Markus Gydesen 40
Kristine Nielsen 37
Ane Marie Gydesen 13
Niels Johansen Gydesen 8,
Else Kjerstine Gydesen 5
Hansine Katrine Gydesen 3
J Murphy