Afraid this is more questions than answers but.. 1860 census of BRISTOL Twp shows Harvey Smith age 56 (b)NY and Hulda age 52 (b)CT The only Gillet children in household were Ellen age 9 and Arthur age 16. Both born OH. Other children not named Gillet were Jesse 14; Albert and either Aaron or Anson (couldn't read it) age 10.
For the heck of it I looked at the 1850 census of Bristol Twp and found only an Augustus B. Gillet age 26 and Eliza age 18. They were born in CT and likely are family to Hulda. Good luck.