I've heard that the family used to act very normal with her. I've got some old books from WWI-time, with pictures of her (and other childrens of the family) inside. You see from the 'young baby'-pics that she had Downs Syndrome, but her mother helds her normal and very proud. The family did send her to a school which cared about the development of disabled children with sports and art and so on.
The picture you show is from her confirmation in 1934.
I don't know if it's okay but I show a link to a postcards seller with some pictures. Please delete if not allowed! :)
Very lovely is the one in which her brother is holding her on the lap.
If you understand german you can find information about her here: Preussen.de - Alexandrine
I have somewhere several pics of Alexandrine. She seemed to be a sweet little girl and a nice adult.