I realize this was posted this some time ago, but I'm just getting into tracing my family and found this today. My ggrandmother was Elizabeth Ann (or Bettie or Betty) Peters Jeffries. I had only heard Bettie until I started looking for records. As you noted, she was the daughter of Mathias Peters and Sarah A. Brown Peters; she was born 13 March 1865 in Hardin, KY, which would have made her 5 years old in 1870 (per your record). I do not know about other children of Mathias and Sarah Peters.
Her sister-in-law, Mary Dina Jeffries (b. 30 May 1862) married George Ralston Peters (b. 19 Jan 1854 in Hardin KY: George was Bettie's brother) on 15 June 1881.
Bettie married James W. Jeffries (b. 28 Mar 1860 in Jefferson, KS) in 1884; they moved from KS to OK around 1900 and settled at Seward, a community between Edmond and Guthrie. Some infant children are buried at the Seward Cemetery.
They moved to Tipton, Tillman Co., OK, where they reared their 4 (or 5?) children. My gmother was one of them: Glennie Mae Jeffries (b. Jul 1888 in Kansas City, Jackson Co., MO); she married my gfather, Grover Cleveland McCormack (b. 27 Mar 1884 in Hopkins, TX).