Judith I recognise the family and it is one I have been covering in my One Name Study, which covers T*BB*T(S) worldwide. I have some dates for the people you mention. One missing piece right now is the 1860 census entries for Edward and family. He married twice, the second wife being Maria, who is dead by 1870.
By the way, I think they were only in CT for a short time, having come from NY and then moved back there in the 1850s. The root of this family is likely to be the RI branch of the TIBBITS family.
Happy to share the data I have. Mail me direct at firstname.lastname@example.org if you wish