Elizabeth Newhall cannot be the daughter of William Hodgkins and Elizabeth Hodgkins unless she is the daughter that was baptized in Lynn, Mass., on Feb. 25, 1727. But with a marriage date of Aug. 21, 1766, this is very unlikely.
From Lynn VR, there are two possible candidates - Elizabeth, d. John, carpenter, and Elizabeth, bp. Oct. 30, 1743. and Elizabeth, d. Benjamin and Elizabeth, bp. Dec. 18, 1743. John & Elizabeth are John "Carpenter John" Hodgkins & Elizabeth Hodgkins I have not found anything for Benjamin Hodgkins & Elizabeth Bennet other than the entries in Ipswich VR of their intention on Oct. 18, 1740, and the subsequent baptisms of their children.
Family Search has that Elizabeth who married Jacob Newhall is a daughter of William Hodgkins and Elizabeth Hodgkins. Unless they had a second daughter named Elizabeth and this daughter was born before about June 1743, it is unlikely that Elizabeth Hodgkins that married Jacob Newhall is their daughter. Add to this, Ezekiel Hunt and Elizabeth, widow Hodgkins, has a son named Joseph who was baptized in Ipswich as "Joseph, s. Ezekiel and Elizabeth, "aged ten years," bp. Sept. 9, 1753." (This entry would have him born before August 1744.)