I found the following family in the 1910 census in Ross Co., Ohio.Things sort of line up with your data and sort of do not.I thought I would pass it on for whatever it is worth:
Census location: Scotts Twp., Chillicothe, 4th Ward district, Ross Co., Ohio Census date: 20 April 1910 Enumeration District: 17 Sheet: 7B Address: 754 (?) Madison Dwelling: 151 Family: 156 JACOB SUMMERS: Head, M, W, 80, Married 50 yrs.; BP(Birthplace): Belgium (German); FBP(Father's BP): Belgium (German); MBP: Belgium (German); Naturalized 1847; Language: German; Occupation: none; Can read, write MARY SUMMERS: Wife, F, W, 67, M. 50 yrs.; 12 children, 9 living; BP: Pennsylvania; FBP: US; MBP: US; Language: English; Wash woman; Can read, write George C (son, 37) Anna (dau., 31) Carl (gson, 12) Leona Fox (dau., 47 or 49) m. 22 yrs.; 2 children, both living Andrew Fox (gson, 18) Harry Fox (gson, 12)
The ages don't quite line up, and "Lana" from the 1880 census would have to be "Leona" from the 1910.Also, Jacob's BP (and those of his parents) in the 1880 is listed as Bavaria, not Belgium.Of course, the information may have been provided by a neighbor and therefore not entirely accurate.Hope that this is of some use.If you think that this is the same family, you might look into naturalization documents for 1847, Ohio.