Since on the 1900 Jackson Co Al census it appears Elizabeth and Norman were just married in Jackson Co Al and her father is shown as being born in TN and mother in Al, I'd do research on these families. The only families I found in Jackson Co 1800/1900 with the husband born in Tn and wife in Al.

1880 Jackson Co Al
Delany Hardin 33 M Tn
Linsey 36 F Al
William 11 M Al
Lisabeth 9 F Al
Margret 7 F Al
Homogenie 6 F Al

1880 Jackson Co Al
Cagle Charlie 43 M Tn Tn Tn
Mahala 36 F Al Al Al
Cagle children..
James Hardin 29 M Tn Tn Tn (son-in-law)
Mary 18 F Al Tn Al (daughter)

1900 Jackson Co Al
Norman Parlier 23 M NC NC NC
Elizabeth 16 F Al TN Al

1900 Jackson Co Al
Delana G Hardin 53 M Tn Tn Tn
Mary E 26 F Al Al Al (wife)
Alice 8 F Al Al Al
Andrew J 6 M Al Al Al
James R 4/12 M Al Al Al

1900 Jackson Co Al
James R Hardin 49 M Tn Tn Tn
Mary 38 F Al Al Al
Charles L 24 M Al Al Al
Nellie 10 F Al Al Al
Thomas 8 M Al Al Al
Joseph C 6 M
Mary A 79 F Tn Tn Tn (mother)
Thomas 17 M Tn Tn Tn (nephew)

Norman W and Elizabeth appear to be in Broad Run, Loudoun Co, Va in 1910 and in Irontown, Lincoln Co NC in 1920. Elizabeth's place of birth is listed as Al in 1910 and TN. in 1920.

Have no proof, just speculation, but it may be a place to start. Hope it helps. No relation.