Apparently Hester Ann Smith (Rector) died in 1862 in childbirth, so probably Matilda was given up for adoption (that is, placed with another family) shortly thereafter. Born in 1859, she would have been only about three years old and could have little or no memory of her biological parents.
Charles Millard Rector died in 1895. Many men in his situation - with many children and a wife who has just died - placed their youngest with other families. In fact I live across the street from an elderly woman who was informally placed in another home, as a baby, by her newly widowed father. It happens.
I didn't post race on some of the census records I posted - did you notice Hester's race?
Below, Jacob's age is off but I think it's the right Jacob Rector (note son Eli)
1880 Washington, Mercer, Missouri Jacob L. Rector 30 born about 1850 Indiana, father born Tennessee, mother born Virginia - color, white Mary L. Rector 29 Rebecca E. Rector 13 Ella J. Rector 11 Lucretia B. Rector 10 William J. Rector 5 John H. Rector 2
Tough now to find Hester's birth and ascertain if she really is Cherokee. However, the story of her heritage seems to be carried along many lines of descendants - and one descendant has a photo of the children in Native American dress (as posted previously).