I didn't find her family on an 1850 Census. It will be difficult to find her mother prior to that because the 1840 Census only shows head of household. The only thing you can do is try to find Jane's death info or when she stops appearing on the Census.
Does Parker & Luvina's marriage license include their parents. If not, I'd look up their newspaper marriage announcement. Both sets of parents might be in that.
I didn't find anything prior to her marriage to Parker.
1880 DeKalb Co. TN
Parker Amonett, b. TN, 41, laborer
Luvina F., b. TN, 35
Andrew, b. TN, 15, works on farm
Thomas H., b. TN, 13, works on farm
Arkansas A. b. TN, 11
James C., b. TN, 8
William A., b. TN, 7
luvera, dau, b. TN, 6
John B., b. TN, 1
Luvina F. "Vinie" Wilson Amonette
Born: 6 Aug 1844
Died: 29 Oct 1891
Buried: Edward Robinson Cemetery, DeKalb Co., TN
The death date is WRONG. See below.
1900 DeKalb Co. TN
Park Amonett, b. TN Aug 1836, M45yrs, farmer
Vina,. b. TN Oct 1840, 8/8 ch
Thomas H., b. TN May 1865, teacher
Jno, son, b. TN Dec 1878, day laborer
Settie, dau, b. TN Feb 1886
Gorden, b. TN March 1889
Wilson, b. TN Oct 1892
J?. B., b. TN Dec 1898
I didn't find Park nor Vina on the 1910 Census. I didn't find their deaths either but TN wasn't recording deaths until 1908.
You can see what the TN Archives has for Dekalb County at http://tnsos.net/TSLA/archives/index.php?county=DeKalb&o...
I'd contact the following and ask if they have a local death index, indexed newspaper death notices and cemetery inventories.
Upper Cumberland Genealogical Association, http://ucga.info/
Justin Potter Library
101 South First Street
Don't every give up. Believe it or not FamilySearch and Ancestry are loading more records every day. (I put that info in our local newsletter so I know.)
You might give it a rest for 6 moths or a year but then look again. Successful Searching!