Laura, I haven't been able to put my Artilla Pedrick together yet with your Pedricks. Through all the 1860, 1870, and 1880 censuses, Artilla and her children are listed within a couple of households of your Pedricks (Hezekiah, William, and Joshua). I firmly believe Artilla was either their sister or a young Aunt. Where there any other brothers? What were their parents names? Do you know when the family moved to Flemington? Where were they before that? I'm hoping I can make a match with an earlier census at least as regards Artilla's age/gender.
I have noticed a posting by a Patty Pedrick who is also searching for ancestors of Hezekiah. Have you been in touch with her?
Please email me at firstname.lastname@example.org directly if you prefer.