As stated, I've not looked at the 1880 census for Newton County, AR, so I don't know if the Dildine family was on it. I'm unaware of which census records you have reviewed, but I would imagine that the family moved sometime between the 1870 census report I've seen and the census report that you've seen. I do know that many families in Arkansas moved from there to Oklahoma just before & just after 1900 during the time frame when Indian Territory land was being opened to white settlers. The Oklahoma Land Rushes are famous.
Harmon Dildine apparently moved from TN to AR about 1861, given the birth states of the children. Given your marriage date of 1850, and the first four children born in TN, it might be said that the marriage was in TN---not OK (unless you have an OK marriage license). This does not appear to be the situation of a second marriage, but rather the 1870 census taker perhaps marking Nancy's birth state as TN in error.
As for Harmon's parents, I really do not know.If you believe that the Harmon on the 1870 AR census is "your" Harmon, you might give serious consideration to contacting Jackie Smith.She has the posting on Dildine GenForum (#2) dated Oct 8, 1998. As you have no doubt seen, the (Harrison or) Harmon, b. abt 1827, on her listing seems to match right-on with this 1870 AR census. To add weight to the connection, Jackie's listing includes a sister Melinda, b. abt 1822,which could very well be the Malinda Dildine, age 50 TN, listed in the household of Harmon on the 1870 AR census. If Jackie's information is good and you can establish a firm connection, then Harmon's parents could be Jonathan Dildine, Sr. and his second wife Nancy (Meelkey) Garrett.
Since you did not mention knowledge of John W. Dildine, I'll take it that you are unaware of his history. If you ever come across anything on him, please let me know.