I initially thought that Turner must be the s/o Buck and Betsy's because of the Turner which is generally a mother's maiden name, as was your thought too. Somewhere I have acquired the date of his birth to be around 1813; this is much to early to be Betsy's child. She married Buck in 1829. (Probably a deduction from the 1850 census showing his age as 37) This census record looks as though perhaps Turner and his family are living with Martha's sister's-in-law(Sarah) and her family. I would have guessed that Martha, maybe died and her sister's husband (also not on the census) It is hard to tell about their last names. (All of them are not listed on the census with last names) Martha Carter 19 is shown on this census and I would think that she would be Turner's daughter, named after his wife. I know this is a lot of supposition, but this theory is as close as I have come. Of course, it IS dependant on his AGE being correct on the 1850 census. All of these Carters were close and two generations could easily be having children at the same time. I am email@example.com
; please feel free to correspond if you have other info about his AGE, or another theory. I still have it in my 'to do' file.