Hi! I'm happy to help with the Thode side, if I can.
I have an Anna Thode, in my tree, that would have been born about the same time as your Anna Thode. Her mother's middle name was Margaretha, so it wouldn't be a stretch that Anna's middle name was Margaretha as well.
Anna's parents are:
Claus Heinrich Thode (1805-1895) of Rendsburg, Rendsburg-Eckernforde, Schleswig-Holstein, Germany and Catharina Margaretha Rohwer (1806-1873) of Rendsburg, Rendsburg-Eckernforde, Schleswig-Holstein, Germany.
Claus H.' parents are:
Claus Thode (1760-?) and Anna Margaretha Böhrnsem (1767-?)
Claus' parents are:
Jurgen Thode (1736-1798) and Elsabe [Maiden name unknown] (1737-1774)
Jurgen's parents are:
Claus Thode (1687-1760) and Abel Martens (1696-1779)
That's as far back as my Thode family tree goes. I hope this helps!