"Hettie" is the nickname for Hester/Esther, and "Hattie" is the nickname for Harriet.  Hettie has a sister, Esther, so we know that isn't the source of her nickname.
"Eliphaz" is a scriptural name pronounced, EL-i-faz (accent on first syllable, short "e").

1.  Marriage Record:

2.  1860 U.S. Census Every-Name-Index/Images (online at Ancestry.com): 
Hetty PORTER (æ 2, b. IL) is living in T7_.R2W, Jackson Co., IL (p. 342), with her parents, Eliphaz PORTER (æ 32, b. OH) & Lucinda (æ 28, b. IL), plus siblings.

3.  1870 U.S. Census Every-Name-Index/Images (online at Ancestry.com):
Hattie PORTER (æ 12, b. IL) is living in Elk Prairie Pct., Jackson Co., IL (p. 94A), with her parents, E.C. PORTER (æ 42, b. OH) & Lucinda (æ 38, b. IL), plus siblings, including a sister, Esther (æ 2, b. IL), so that's not Hattie's name.

4.  1880 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #14 of 19):  Linn, Woodford Co., IL, Roll 262, p. 390B, PN 14, SD 4, ED 224, enumerated 23/24 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	8	9	10	13	24	25	26
130	130	Corbin James	W	M	26			/	Farmer	IN	OH	SCT
		______ Hettie M	W	F	23	Wife		/	Keeping House	IL	IL	OH
		______ Joseph	W	M	21	Bro	/		Farmer	IN	OH	SCT

5.  1885 Nebraska State Census Every-Name-Index [no images]. NARA, Washington, DC (online at Ancestry.com; this is a person-by-person extraction, they are not grouped in households):  Clay Twp., Pawnee Co., NE,  Roll M352_41, p. 10:

Janes CORBIN	31	IN
Hette CORBIN	27	IL
Sylva CORBIN	2	NE
Roy CORBIN	4m	NE

6.  1890 U.S. Census:  the 1890 Census Population Schedules were destroyed.

7a.  1895 Nebraska State Census — there was none.

7b.  1895 Kansas State Census Every-Name-Index/Images.  Kansas State Historical Society (online at Ancestry.com):  not found.

8.  1900 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #10 of 14):  Coleman Twp., Washington Co., KS, Roll 503, p. 60B, SN 14, SD 5, ED 131, enumerated 22 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

19

20

21

22

23

24

25

27

28

249

252

Corbin James

Head

W

M

Apr 1854

46

M

22

IN

OH

SCT

Farmer

0

Y

Y

Y

O

F

230

______ Hetta

Wife

W

F

Sep 1857

42

M

22

4

4

IL

OH

IL

Y

Y

Y

______ Sylvia

Dau

W

F

Apr 1884

16

S

NE

IN

IL

8

Y

Y

Y

______ Roy Allen

Son

W

M

Feb 1885

15

S

NE

IN

IL

8

Y

Y

Y

______ Edna Pearl

Dau

W

F

Nov 1886

13

S

NE

IN

IL

8

Y

Y

Y

______ Ruby Irene

Dau

W

F

Jan 1895

5

S

NE

IN

IL

Y

Y

Y

9.  1905 Kansas State Census Every-Name-Index/Images.  Kansas State Historical Society (online at Ancestry.com, Image #5 of 66):  Linn P.O., Coleman Twp., Washington Co., KS, Roll ks1905_168, p. 4, official enumeration date 1 Mar 1905 (extracted by Diana Gale Matthiesen):

1905:  for an explanation of the column headings, please see What the Numbers in the Census Mean (columns 19-24 contained no data).
Ln	1	2	3	4	5	6	7	8	9		10	11	12	13		14	15	16	17	18
23	O	M	H	15	15	Corbin James	51	M	W		Ind	Neb	Farmer
24						"   Hettie	47	F	"		Ill	"
25						"   Edma	18	"	"		Neb	"
26						"   Ruby	10	"	"		"	"					7
27						Porter Lucinda	73	"	"		Ill	Ill

Lucinda (PARRISH) PORTER is Hettie's widowed mother.  Listed two households from C.M. [Charles Maxmillian] DAMETZ, brother of Lucinda (DAMETZ) THOMPSON, future mother-in-law of our subjects' son, Allen Roy CORBIN.

.  1910 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #

.  1915 Kansas State Census Every-Name-Index/Images.  Kansas State Historical Society (online at Ancestry.com, Image #

.  1920 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #

.  1925 Kansas State Census Every-Name-Index/Images.  Kansas State Historical Society (online at Ancestry.com, Image #

.  1930 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #

.  LDS Family Search:  Pedigree Resouce File (online at familysearch.org).

.  Public Member Trees (online at Ancestry.com).

.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).