In 1870, she's a 2-year-old in the "Champaign County Infirmary" and identified as "insane". How a 2-year-old could be insane is, well, nuts.
I can't find her in 1880. Not in Ohio anyway. There's a family of Leggs in Virginia, mother Catherine (which could be "Kate" in other records). Do you have any siblings for her?
I presume she's the one who married Hamlin.
Have you made any effort to obtain a birth record for her? Or marriage record? Do you know what faith she practiced? You might find church records microfilmed by the LDS...