I can offer information about the medal itself and what it was for, how it was awarded, etc. I have nothing to offer on the signature on the back. The other text on the back is German for 16 December, 1938, the date the award was created.

The medal, you correctly state, was an award for German mothers who bore numerous children. It was the Ehrenkreuz der Deutschen Mutter, the Cross of Honor of the German Mother, often shortened to Mutterkreuz, Mother's Cross. In short, it was one of the ways the Nazi regime encouraged German parents to have large families. Benefits of having such a medal included greater respect and social standing. Hitler Youth would salute mothers who displayed their medal, for example.

The award, in three levels of Bronze (4-5 kids), Silver (6-7), and Gold (8+), was created in December, '38 and awarded through the end of the war. Candidates were eligible by having multiple kids, as stated, but also by displaying the ideal qualities Nazi ideology espoused. Among these qualities were: having German blood (so, both parents do not have non-German, especially do not have Jewish grandparents); good "moral standing" (e.g. not a prostitute, no interracial relationships, no abortions); the husband hasn't been in prison/isn't a criminal, and so forth.

Among the reasons for the creation of this award included the Nazi position on procreation (i.e. more Germans in the world, the better) and reasons to want a larger population (anything from more Germans means greater chance the "Aryan race" survives, future soldiers for future wars, things like that), as well as a means of social control: the 1920s Weimar culture saw a lot of changes in traditional gender roles. If women were working or not marrying, being more sexually open, etc. then they likely were not being housewives raising many fat children. Nazism isn't known for its open and respectful views toward women. Simply put, Nazi ideology sees women serving the state via raising a (large) family; men, in turn, serve the state by fighting for it. The motto Kinder, Küche, Kirche sums it up: Children, Kitchen, Church.

I'm pulling this summary largely from memory, but I looked through a few relevant articles I have saved from my German history courses in college that focus on Nazi family policy and sexism and the like, should anyone be interested in further reading. I can dig further if anyone would like more sources:

• Rupp, L. (1977). Mother of the "Volk": The Image of Women in Nazi Ideology. Signs, 3(2), 362-379.

• Bock, G. (1983). Racism and Sexism in Nazi Germany: Motherhood, Compulsory Sterilization, and the State. Signs, 8(3), 400-421.

• Gupta, C. (1991). Politics of Gender: Women in Nazi Germany. Economic and Political Weekly, 26(17), WS40-WS48.

I hope this has been helpful!

Edit: grammatical clarity.