Information on the children of Andrew & his second wife Betsey, as well as the date of Andrew's first marriage, came from Linda Poast. She mentioned the source as an Adams Family Bible extract published in the Vital Records of Greenfield, MA.
These records are also available online at newenglandancestors.org
Andrew was of Northbridge, MA, when he married his second wife Betsey.
I am fairly sure that these records pertain to this particular Andrew Adams:
1759 ADAMS Andrew, h. Molly (Morse), h. Betsey (Chapin), Nov. 7,1759, in Sutton ("now Northbridge"), Worcester Co., P.R.28. Birth Greenfield
1759 ADAMS Andrew, s. John of Uxbridge, bap. Dec. 9, 1759. C.R. Birth Grafton