I've recently been doing more research on the Mondientz family, particularly Adolph Mondientz and his career in theatre.
I have found that Heinrich Heine Universität Düsseldorf has, in their digital collections, some theatre posters for the Stadt Theatre in Düsseldorf for the years 1860 and 1861. Amongst these are a number which reference members of the Mondientz family, namely Adolph Mondientz, Emma Mondientz, F. Mondientz, and Marie Mondientz.
Adolph Mondientz is listed for all the acting roles he performed in many different plays, his daughters Emma and F (who would be Franciska) play child roles in a few of the plays, and then we have Marie. I can't work out who she is in the family because Adolph did not have any children with Marie in their name. She is only in one of the plays that have posters in the digital collection: Die Waise aus Lowood (Jane Eyre) where she performs in two productions, as Adele; the character being a young child of about 9 years old. So she must have been a child, but whose?
I suspect she might have been a cousin of Adolph's children, either a daughter of one of his brothers, or of one of his sisters, out of wedlock (hence the surname Mondientz), though I haven't found anyone that fits the bill yet. I haven't managed to find any birth record--or anything else, for that matter--for a Marie Mondientz at this stage either, so we are left to wonder.