Verena,
I know that your posting is almost five years old and you may have already found the information you are looking, but are you still seeking information about Johann Jakob Frei who was born on the 23 July 1779 in Eichstetten? I think I located some Eichstetten church records about him while I was doing some research of the Danzeisen families in Eichstetten, as the Frei and Danzeisen family lines cross over to each other.
It looks like Johann Jakob Frei was married twice – first to Katharina Josslin and then to Maria Kehl.
Christian’s mother was Katharina Josslin and he was born 28 Oct 1820. Christian married Christine Frei a couple of years prior to their departure for the US.

I am not sure if this fully fits what you are looking for or not.