Greg: According to the Cudworth Gen. all your info is correct.Lydia is listed as "Lydia TOWER (perhaps a widow)".She and Joseph had 4 children all settled in Bristol, ME. She d. before 1775.Joseph remarried 9 Mar. 1775 Elizabeth SOUTHER of Cohasset.
The Capt. Joseph CUDWORTH you referred to may be the son of Lydia and Joseph. b. 17 Oct. 1795 m. 1795 Betsey CLARK of Bristol, ME. He is listed as the first of a long line of sea Captains sailing from Maine.Joseph his father was a prominent shipbuilder in Scituate.
Interesting note the 2nd family descendants had no knowledge of the 1st family after several years.