You asked (and stated): "...BUT both William and his wife are on their 2nd marriage. So, who is the mother of Martha C. Smith. Is it the same person as listed in the 1880 census or not!
It was not uncommon for married children to live next to OR nearby the parents in the early 20th century...."
Sorry it has taken me so long to respond to your message here.I've been working this line for several years now.
Martha C. Smith was born 1 Jan 1880. (Headstone inscription, Add Smith Cemetery, Rhea County, Tennessee)
William Addison Smith and Eliza Jane Minick were married 27 May 1877 in Rhea County, Tennessee. ("Tennessee, Marriages, 1796-1950" GS Film number 589468)
By virtue of the dates she would appear to be the product of their marriage.
This is supported in her death certificate where her parents are listed by informant C.L. Trentham (I'm pretty sure this is Chapman).("Tennessee, Death Records, 1914-1955", Image Number:01822, GS Film number: 1876745)
Martha died from complications from a carcinoma of her jaw.