Yes, the family are still in Rantzausminde/Egense in 1911.
" Maybe she was a maid in Svendborg, got pregnant, and came to copenhagen then? " This is exactly what I'm guessing, this is the theory I'm working after and why I want to search the entire Svendborg Amt 1911. I also planned to look through the churchbook for Den Kgl. Fødselsstiftelse, maybe she did have an earlier pregnancy. So you thinking the same as me, gives me a little hope, that maybe I am on the right track.
Magda is not the mother of my grandmother, but her aunt. The story was told to my grandmother by her mother Ebba, the halfsister of Magda, who was very close to her.
When Ebba died my grandmother continued writing with Magda until Magdas death. During all those years of corresponding, the story never changed, so it's almost like quoting Magda.
Thank you very much for your input, if you have any other ideas please let us know.