According to The Dana Family in America (Eliz. E. Dana, 1956) at p. 412 (https://www.seekingmyroots.com/members/files/G001616.pdf), a different Joseph Dana is the father for this Daniel Dana (d. 1881). The family book asserts that Joseph Dana (1803-1834 of Athens Ohio) is his father (p. 358), rather than Joseph Dana (1769-1849, also of Athens, the father of the naval commander, Wlm. Henry Dana). See pp. 300-302 The same book asserts that this Daniel Dana was born in 1832 rather than 1836.
If you have time to look into it and form an opinion, please advise.