Anna Margarethe Magdalene Petersen's mother was Anne Christine Petersen born 6 Jan 1859 to Peter Petersen and Maren Schmidt. She died shortly after Anne Margrethe's birth on Mar 10 1891. Other children were Peter - b. 13 June 1880, Marius -b. 23 Dec 1881, Frederik -b. 10 April 1885, Valdemar -b. 29 June 1887 and Jes -b. 5 Mar 1889
I found Anne Margarethe's birth record in the parish records for Aller Sogn, Haderslev. And also her mother's death record. If you're interested in having copies send me a note and I'll be happy to forward them to you.