Elisha Shaw and Susannah Clark declared their intention of marriage 11 Dec 1743 in Weymouth, MA (perhaps married in Braintree).
David Turner Shaw's brother Joshua Shaw was born 17 May 1755 perhaps in Braintree (Maine Families in 1790 state he was born in Weymouth, son of Elisha Shaw and Susanna Clark). If you are correct Susanna lived until 1790, she would also be the mother of David Turner Shaw.
On the 1790 U. S. Federal Census in Maine, Elisha Shaw and Elisha Shaw Jr are living in Littleborough Plantation (now Leeds); David and Joshua are living in Bath Town.
I don't know where you found Hannah, though I have occasionally seen the name Susannah with the nickname Hannah or Anna in the 1600s/1700s.
I have Susanna Clark born 17 Nov 1724 Braintree, though haven't verified this with a vital record.
Other than some of Joshua's descendants, I have little on this family.