Catherine Elizbeth is likely the granddaughter of J. Phillip Steinman, probably through his third son Louis Stineman.
The patrilineal descent to Phillip is: Hans, Phillip (b. 1609), Peter (b. 1648), Barthel (b. 1676), Johann Peter (b. 1703), Johann Jakob (b. 1744), Johann Philip (b. 1775).
J. Philip and Anna Marie Marquadt Steinman had six known children:
1. Johann Peter Steinmann, born March 21, 1803
2. Johann Philip Steinmann, born Mary 13, 1804
3. Eva Maria Steinmann, born April 4, 1807
4. Johann Ludwig Steinmann, born February 2, 1810
5. Anna Maria Steinmann, born February 18, 1813
6. Elisabeth Barbra Steinmann, born July 5, 1817
The three sons emigrated to America and had the following children:
1. J Peter Steinman married Catherine and immigrated to Vermilion in Erie County, Ohio. Children: a) Peter born 1837, b) Matilda born 1839, c) Ele J born 1841, d) Joseph born 1843 e) John E born 1845, and f) Solomon born 1848,
2. J Philip Steinman/Stineman married Margaret Buster in Pennsylvania in 1832. They first lived in Pennsylvania, removed to Ohio in 1833-1834, then to Iowa in 1856.Children were a) Henry born 1833, b) David born 1834, c) George born 1836,d) John born 1838, e) Mary born 1840, f) Catherine born 1842, g) Sarah born 1845, h) Margarett born 1847, i) Elizabeth born 1849, and j) Martha born 1853.Henry was born in Pennsylvania, the rest in Ohio.
4. J Ludwig, aka Louis (Lewis) Stineman.Mau havemarried Elisabeth Rett, mother of a) Andreas Steinmannmentioned in an earlier post. Andreas remained in Germany.Louis then married Eva (Eve) Elizabeth Rettig .Their children were b) Betsey born 1843, c) (John) Peter born 1844, d) Elizabeth (Eliza) born 1846-1847, e) Margaret (Maggie) born 1852 and f) Louis Henry born 1855.Betsey, Peter, and Eliza were born in Gadernheim in Hesse-Darmstadt, which is close to Baden-Württemberg.Margaret and Louis were born in Ohio.The family moved to Grandview, Iowa around 1856 where Eve Stineman died in 1857.Louis married a last time to Nancy A. Trimble Wallace and had a son g) Isaac Elsworth, born after 1860 in Iowa.
Not sure where your Eliza Catherine.She is probably not 1. J. Peter and Catherine's daughter, as she was not living with them in the 1850 census and they never moved to Grandview, Iowa.She is probably not 2.i) Elizabeth Stineman born 1849 in Ohio.She is probably not 4.d) Eliza, daughter of Louis and Eve, unless you have her birth year off by a decade.She may be the daughter of a cousin of Peter, Philip and Louis Stineman.A John Steinman lived in Ohio, near the others.Hope this helps a bit.