I have not been able to find this family in 1870 either,
BUT I am wondering if perhaps Samuel and Sarah were not yet married in 1870.
The children could be either his from a first marriage or hers from a previous marriage.
If so, they may not have been born as SCOTT.
I am thinking this because I found a Samuel Scott in 1870 who fits for age and birthplace.
1870SALT POND, SALINE, MO SCOTT Samuel M., age 40 born TN
Mary F., age 24, born VA
Mina A., age 7/12, born MO
AND in 1880 Samuel is NOT with this wife and family
1880 LIBERTY, SALINE, MO SCOTT Mary F., age 34, widowed, born VA parents born VA
Mina, age 10, daughter born MO father born TN mother born VA
Joseph, age 8, son born MO father born TN mother born VA
Ettie, age 5,daughter, born MO father born TN mother born VA
MEADE Alice, age 39, boarder, cousin, born VA father born NY mother born VA
Mary is shown as widowed but it was not uncommon for women to state they were widowed when they were divorced or their husbands had left.
If this is the same Samuel and he later married Sarah - it seems likely that the only child of Samuel and Sarah was Elizabeth - note -the large gap in ages between Alexander born about 1871 and Elizabeth born about 1880 -
So I went to 1870 census to try to find Sarah and children - no luck so far
I tried looking for them using Harvey and Price names as they are the most unusual of the bunch but no luck at all.I wonder if they were their middle names and they are listed under first names in 1870 census ???