You're on the right track.The spelling of Shatto on the 1870 OH Noble Co, Center Twp. report could be Shatton or possibly Shattow, but definitely this is a Shatto family.
Interesting question and a great puzzle. Just what the connection is between the Carrolls and the Shattos is not clear.
The 1870 Center Twp, Noble Co OH census shows Caleb Shatto aged 20 and Margaret Shatto aged 6, with Sarah Carroll aged 57.
Neither Margaret nor Sarah Carroll show up in Caleb's census report of 1880.However they show up right next door in a separate household as Sarah "Carl" aged 66, widowed, and Margaret Shatto, granddaughter, aged 17 in OH Noble Co Center Twp..And then the next household is Thomas Shatto, aged 41, with wife Nancy (Johnson) and family.Said Thomas Shatto and Caleb Shatto are first cousins, both grandsons of Nicholas Shatto and Jane Patterson.
Thus one reading of relationships is Sarah Carroll the grandmother, Caleb Shatto the father (but a very young one), and Margaret the daughter.This reading assumes that Caleb is a widower and that his first wife was a Carroll - but this stretches crdulity a bit.
Alternately, Sarah Carroll is definitely grandmother to Margaret Shatto but her relationship to Caleb is not crystal clear.
Another possibility is that Caleb's father, Andrew Shatto, had a sister Sarah Shatto, b. 1809.She married a William Ambler who died in 1856, Pike Co OH. - but no information about whether or not any of her daughters married a Shatto in order to produce Margaret Shatto, of Caleb's 1870 census report.
Caleb married Mary C. "Kate" Johnson Aug 09, 1870, in Noble Co, by whom he had at least three children - all of whom appear in his 1880 OH Noble Co Center Twp. census report
Now the question of the Sarah Shatto who married John Carroll in 1852.I am tempted to speculate that Sarah Shatto is the same Sarah Carroll as above, but the date of marriage to John Carroll is a bit late for her to have had a daughter who married Caleb Shatto and also be the mother of the above Margaret Shatto b. about 1863 ... unless it is a second marriage for Sarah Shatto.
Question.Do you have any idea about the parents of this Sarah Shatto or any other information about her??It very well could be that Shatto is not her maiden name and the 1852 marriage to John Carroll is her second marriage.