My father's great grandfather was Johann Peter Buechele (1803-1863) born in Boennigheim, Besigheiw, Wuttemberg died in Vanderburgh County, Indiana. Came to US in 1841. His daughter Katharine Johanna A (Hannah, Johana) was born 10 Nov 1838 in Boennigheim and died 25 Jul 1914 Louisville, Jefferson, Ky. She married Conrad W Hafendorfer on 12 Sep 1860 in Evansville and they had 7 children.. Buried at Cave Hill Cemetery, Louisville, Jefferson County, Kentucky.
According to the daughter Adeline of your Peter in her 1870 Census report her father was born in Wurttemberg. I am almost sure that he was not in my direct line and am almost sure he was not a son of the father of my Johann Peter who was also Johann Peter. Maybe he was a cousin of my Johann Peter since he was about the same age. If he were it would have been from Johann Conrad b. 25 Oct 1763 or Johann Jacob b 7 Jan 1756 both in Boennigheim At that time Buechelin was often used for some of my people - I don't understand why.
If this helps, let me know.