I don't know if this is your Houston Alexander; however, I just discovered the will of William Alexander dated ca. 1831 in Warren County, TN (Warren was divided into several other counties including DeKalb and Cannon around 1836).
William names his wife as Martha. He doesn't really name his children.....he just states that when his wife dies everything is to be sold and divided equally among "our children."
He then states that ..."200 acres of the land he purchased from (I can't read the name) is to be given to James Alexander and the rest to be given to HOUSTON ALEXANDER."
It just isn't clear if these are his sons or not....but they must be related in some manner....they could be brothers or nephews.
I do know that William first appears on the Warren County tax rolls in Graham's District in 1812. He is also on the census in 1820 and 1830. His wife Martha is head of household on the 1836 tax rolls.
I am trying to sort out all the Alexander's in early Warren County....determine the sons from the fathers. I have a list of all the names .... if you find anything that might help...please let me know.