If your only source for Caroline is the IGI record which provides no clue to who submitted the information or any way to check its reliability, I would not rely on that. The IGI is often inaccurate. I've seen numerous errors with women having children at age 85, or men fathering children many years after their death. Although the IGI can provide clues, the information needs verification.
Since there was a Caroline Dyer the right age in Hollis Maine on the 1850 census, I would consider that as a possibility. The website for the Dyer Families of New England does not have parents for her, but they also don't have a spouse for the Caroline Dyer who was daughter of Seth Dyer and Mary "Polly" H. Lane.
I also wouldn't rely on "The Book of Dow" without knowing the source of the entry. I agree that based on the 1850 census, Daniel, son of Jeremiah does not look like a good possibility. However, I have seen many incorrect ages on census records, so it is possible that the 1850 census has the wrong age. It might be worthwhile to see if there is a birth or marriage record in ME or a death record in MA or PA. Caroline is a widow in 1880, so that narrows the time frame for Daniel's death.
In 1880, Caoline is still saying she was born in ME and both parents were born ME, so I would think it unlikely she was b. Scotland.
There are 6 Dow families in York Co. ME in 1840 and about a dozen in 1850. In 1850, Biddeford, Jeremiah was actually indexed as Jeremiah Den, not Dow, and include Phebe and 9 children ages 3 through 21. Because of indexing problems and only head of household named prior to 1850, I doubt that earlier censuses will be much help.
I have no first-hand information on this Dow line, but it looks to me like you will need to obtain some official birth, marriage, or death records, or locate an obituary, etc. to resolve the question of both Caroline and Daniel. I don't think either the book or the IGI entry is on the right track!