According to "The Book of Dow" Daniel was the son of Jeremiah Dow and Phoebe Young of Biddeford ME.The 1850 census does have Jeremiah and Phoebe with a son Daniel but has his age as 16. Both the 1860 census and the 1870 census show Daniel, Caroline, Francis and William in Newton MA, and give ME as birthplace for all 4. Are you sure of Caroline's birth place? The book gives her birth as Hollis ME. There is a Seth Dyer family with Caroline age 11 in 1850 census of Hollis ME.
In 1860 Caroline is listed as 31 and Daniel as 42. William is 6, and Francis is 2. In 1870, Caroline and Daniel are both 42, Wiliam is 16, and Francis is 11.