It's a bit hazy in English now with the difference between should/shall/am supposed to. Shall is almost dead and should appears to be replacing it. Shall/Should I open the window? This is different to should/am supposed to: I should/am supposed to be working. Similar uses and meanings.
What's wrong with "You shall eat!" I'm a native British English speaker, and when I saw the German, this is what I assumed the translation would be. "You are supposed to eat", does not mean the same thing. [Guests] "We don't feel right eating your party food, as we weren't actually invited." [Host] "You shall eat!"