It does look like we are related. My next step is to confirm Sara's marriage to William Smith Peckham (1793, no location given).
Do you have any information on when and where Charles lived in Ohio? Eunice was born in Jefferson Co. Ohio and died in Scioto Co, Ohio.She is buried in Pine Grove Cemetary along with her husband Samuel Miller. I don't know when Sara and William moved out to Ohio.
I'd love to see what you have collected on the Peckham family.After I found the information on the LDS site, I went to the Rhode Island GenWeb site and read a little about the early Rhode Island Peckhams.
As soon as I can determine what I'm looking for I can hopefully take some time to get out to Rhode Island.Let me know if you have specifics you are looking for there.
I will email you my home address as soon as I post this. Look forward to hearing from you!