The second marriage date cannot be correct because they are both still unmarried in the 1910 census.

1a.  Michigan Marriages, 1822-1995 (online at familysearch.org):

Groom's Name:	John A. Van Arkel
Groom's Birth Date  | Age | Race:	1875 | 33 | White
Groom's Birthplace:	Netherlands
Groom's Marital Status:	Unknown
Bride's Name:	Ada R. Strong Sherman
Bride's Birth Date | Age | Race:	1872 | 36 | White
Bride's Birthplace:	Mich
Bride's Marital Status:	Widowed
Marriage Date:	15 Sep 1908
Marriage Place:	Allegan, Allegan, Michigan
Groom's Father:	Walter Van Arkel
Groom's Mother:	Catherine Vinkelberg
Bride's Father:	Thomas Strong
Bride's Mother:	Caroline Hoyer
Bride's Previous Husband's Name:	Sherman
Source Film:	1017877

"Strong" is undoubtedly a misreading of "Stroup."

1b.  Michigan, County Marriages, 1820-1935 (online at familysearch.org):

Groom's Name:	John A Van Arkel
Event:	Marriage
Event Date:	09 Oct 1928
Event Place:	Kalamazoo, Michigan
Age:	53
Father:	Walter Van Arkel
Mother:	Katherine Finkelberg
Spouse:	Ada Straub
Spouse's Age:	54
Spouse's Father:	Thomas Straub
Spouse's Mother:	Caroline Moyer
Digital Folder:	4674178

Did they remarry?  Or was the record misread?

2.  1900 Census Every-Name-Index/Images (online at Ancestry.com, Image #15 of 16):  Columbus Twp., Van Buren Co., MI, Roll T623_745 (Book 2), p. 115A, SN 8, SD 4, ED 137, enumerated 15 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	16	17	18	19	20	22	23	24	25	27
187	187	Van Arkel John	Head	W	M	Jun 1874	25	M	1			Holland	Holland	Holland	1882	18	Na	Jeweler	2	Y	Y	Y	R	H
		_________ Catherine	Wife	W	F	May 1878	22	M	1	1	1	Michigan	Germany	Germany				Keeping House		Y	Y	Y
		_________ Baby	Son	W	M	??? 1900	2/12	S				Michigan	[unreadable]	Michigan						Y	Y	Y

3a.  1910 Census Every-Name-Index/Images (online at Ancestry.com, Image #5 of 32):  122 Second Street, Allegan City (Ward 2), Allegan Co., MI, Roll T624_634 (Book 1), p. 176A, SN 3A, SD 4, ED 2, enumerated 16 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):¤•

1910:  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	16	17	18	19	20	21	22	23	24	26	28
*	122	70	73	Van Arkel John A	Head	M	W	32	M2	2			Holl Dutch	Holl Dutch	Holl Dutch	1885	Na	Eng	Proprietor	Cigar store	Emp			Y	Y	R	H
				_________ Ada	Wife	F	W	38	M2	2	0	0	Michigan	Michigan	Ohio			Eng	None					Y	Y
				McGinn John	Boarder	M	W	56	M1	8			New York	Ire English	Ire English			Eng	Salesman	Cigar store	W	N	12	Y	Y
*Second Street

3a.  1910 Census Every-Name-Index/Images (online at Ancestry.com, Image #13 of 15):  Columbia Twp., Van Buren Co., MI, Roll T624_676, p. 225A, SN 7A, SD 4, ED 145, enumerated 4-5 May 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):-

1910:  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

16

17

18

19

20

23

24

25

26

27

28

29

168

172

Malkuska Charles

Head

M

W

67

M1

40

Germany (Ger)

Germany (Ger)

Germany (Ger)

1876

Na

Eng

Farmer

General farm

OA

N

N

O

F

F

112

________ Annie

Wife

F

W

72

M1

40

6

5

Germany (Ger)

Germany (Ger)

Germany (Ger)

1876

Eng

None

Y

Y

Van Arkel Katy

Dau

F

W

32

Wd

2

2

Michigan

Germany (Ger)

Germany (Ger)

Eng

None

Y

Y

_________ Walter

GSon

M

W

10

S

Michigan

Unknown

Michigan

Eng

None

Y

Y

Y

_________ Pauline

GDau

F

W

6

S

Michigan

Unknown

Michigan

None

Y

Back then, being divorced carried a considerable social stigma, so it would not be at all unusual for both parties to afterwards claim to be widowed.  My own grandmother did the same in the 1900 census.

4.  1920 Census Every-Name-Index/Images (online at Ancestry.com, Image #10 of 17):  Alamo Twp., Kalamazoo Co., MI, Roll T625_775 (Book 1), p. 5B, SN 5B, SD 147, ED 140, enumerated 17-19 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):¤•

1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
2	3	4	5	6	7	8	9	10	11	12	13	14	17	18	19	20	21	22	23	24	25	26	27	28	29
Fm	134	135	Van Arkel John	Head	O	M	M	W	42	M	Un	Un	Y	Y	Holland	Dutch	Holland	Dutch	Holland	Dutch	Y	Farmer	General Farm	OA	96
			_________ Ada	Wife			F	W	52	M			Y	Y	Michigan		Michigan		Ohio		Y	None

5a.  1930 Census Every-Name-Index/Images (online at Ancestry.com, Image #7 of 19):  Alamo Twp., Kalamazoo Co., MI, Roll 997 (Book 1), p. 104A, SN 4A, ED 39-1, SD 16, enumerated 10 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):¤•

1930:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
3	4	5	6	7	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	30	32
90	91	Van Arkel John A	Head	O	R	Y	M	W	54	M	23	N	Y	Holland	Holland	Holland	Dutch	1880	Na	Y	Farmer	General Farm	O	Y	N	78
		_________ Ada	Wife				F	W	54	M	32	N	Y	Michigan	Ohio	Michigan				Y	Nurse	Private cases	W	Y

5b.  1930 Census Every-Name-Index/Images (online at Ancestry.com, Image #17 of 72):  712 W Lovell St., Kalamazoo City (Ward 3), Kalamazoo Twp., Kalamazoo Co., MI, Roll 997 (Book 2), p. 61A, SN 9A, ED 39-24, SD 16, enumerated 8 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):¤-

1930:  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	11	12	13	14	15	16	17	18	19	20	24	25	26	27	28
*	712	142	243	Exner Ella	Head	R	35	R	F	W	53	S		N	Y	NY	NY	NY	Y	Teacher	Public school	W	Y
				_____ Lavina	Mother				F	W	77	Wd		N	Y	NY	NY	WI	Y	None
				VanArkel Ada	Lodger				F	W	50	M	30	N	Y	MI	OH	OH	Y	Housekeeper	Private home	W	Y
*W Lovell St

Apparently Ada sometimes worked out for a client.  There's no obvious genealogical connection between Ada and Louvina (WALL) EXNER.

6.  Michigan Deaths and Burials Index, 1867-1995 (online at Ancestry.com):

Name:	John A. Van Arkel	Ada Rachel Vanarkel
Birth Date:	abt 1876	27 May 1869
Birth Place:		Allegan Co.
Death Date:	10 Feb 1949	7 Jun 1946
Death Place:	Coloma, Berrien	Otsego City, Michigan
Burial Date:		10 Jun 1946
Cemetery Name:		Oakwood
Age | Gender | Race:		77 | Female | White
Occupation:		Wife
Marital Status:	Married	Divorced
Spouse's Name:	Kate Van Arkel
Father's Name:	Walter Van Arkel	Thomas Straub
Father's Birth Place:		Ohio
Mother's Name:	Catherine Finklenberg	Caroline Hoyer
Mother's Birth Place:		Ohio
FHL Film Number:	1954927	2110085

7.  World War I Selective Service System Draft Registration Cards, 1917-1918.  Microfilm Series M1509 (4277 rolls), National Archives and Records Administration, Washington, DC (card images and index online at Ancestry.com):

Microfilm Roll:	1675113
Name:	John Anthony Van Arkel
Permanent Home Address:	126 N Farmer St Otsego Allegan Mich
Age in Years | Date of Birth:	43 | June 26th 1875
Race:	White
U.S. Citizen:	can't read
Present Occupation:	Prop. Billiard Room
Employer's Name:	Self
Place of Employment:	Otsego Allegan Mich
Nearest Relative: Name:	Mrs. Ada Van Arkel
Nearest Relative: Address:	126 N Farmer St Otsego Allegan Mich
Signature:	John Anthony Van Arkel
Height (tall, medium, short):	Tall
Build (slender, medium, stout):	Medium
Color of Eyes | Color of Hair:	Brown | Gray
Physically Disabled:
Date of Registration:	Sept 12th, 1918

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