I have 4 branches of my family are from Germany. In 1870 There was a war going on and a great deal of Germans immigrated because of it. Some regions of germany were ruled by Denmark and France depending on the time. My Roots are in the Schleswig-Holstein state of Prussia. From what you have given me your roots are in the Hessen State.
What I have discoverd is because of the wars and political unrest of the area in that time, it is difficult to trace but not impossible. I did find some info at The church of latter day saints from a different branch. They have an extensive geneology library. Some of the search can be done online some of it needs to be done at there history libraries all over the world. It will help a great deal to know what region or state Manderbach was located. (Hessen State) I think is was called Back then, Most of germany was called, Prussia. You can look up on the internet prussian maps (year).
The Braas side of my family were from Nottfeld and Bohnert Germany. In 1767, That part germany was under the Danish flag. The Braas roots were actually Danish not German.
Their was an Anna Elizabeth born 1802 but lived only a month and her parents are not the ones you have listed.
The video for researching german roots is invaluable on the link below. it is about 48 minutes and will worth watching it. It has great hint and clues on how to continue your search.http://www.familysearch.org/Eng/Library/FHLC/frameset_fhlc.a...http://www.familysearch.org/eng/library/education/frameset_e...
There is a page on ancestry Progeneaologist will give you some vauable info. If you can't click on the link you can copy and paste it to your url. There is some great information. This link is on ancestry.com and will be needed for researching German roots. It lists some info you will need. It is from the Gazetteer M / Progeneaologists on Ancestry.comhttp://www.progenealogists.com/germany/hesse/hessnasM.htm
This link wil give you some much needed info on where to continue your search.
If I find out anything more I will let you know.