In many of the deeds transferred after Diodate died, George Calkins is listed as the executor of his estate (later this position was taken up by Arthur Cogswell). Diodate may have had a daughter (or even grand-daughter) named Lydia M. Clark, as there is one listed as having married George Calkins in Cuyahoga County, Ohio.
CLARK, LYDIA M and CALKINS, GEORGE vol.0004 pg.0503
Diodate had a sister named Lydia, but she was known to have married Sylvanus Brooks who then married another sister when that Lydia died, so it is very unlikely that it was Diodate's sister who married George W. Calkins.

From the 1880 census:
George CALKINS1 Self M Male W 54 VT Lime Kiln & Store VT VT
Lydia CALKINS2 Wife M Female W 52 CT Keeping House CT CT
Charles C. CALKINS3 Son S Male W 25 OH Manager Lime Kiln Co VT CT
Harry W. CALKINS4 Son S Male W 22 OH Boat Keeper VT CT
Burt W. CALKINS5 Son S Male W 18 OH Foreman VT CT
Caroline KELLOGG6 SisterL W Female W 48 CT At Home CT CT
Mary GRAHAM7 SisterL D Female W 42 CT At Home CT CT
Fanny L. GRAHAM8 Niece S Female W 15 OH At Home CT CT

Another possible daughter of Diodate (listed in above census as George's sister-in-law):
CLARK, CAROLINE and KELLOGG, HORACE 0004 0315
Obituary:
Name: Kellogg, Caroline Lavinia
Date: August 3, 1908
Source: Source unknown; Cleveland Necrology File, Reel #044.
Notes: Kellogg-Caroline Lavinia, widow of Ensign H. Kellogg, and mother of Mrs. William E. Cushing, at her home in Pittsfield, Mass. on Friday, July 31.

An obituary for Lydia (Clark) Calkins was also found, though it gave no clues as to who her parents were:
Name: Calkins, Lydia M.
Date: November 27, 1911
Source: Source unknown; Cleveland Necrology File, Reel #012.
Notes: Calkins-Lydia M., wife of George W. Calkins, at the residence of her son, Henry W. Calkins, Toronto, Canada. Funeral services at the chapel, Lakeview cemetery, Monday, Nov. 27, at 11 a. m.
And one for George:
Name: Calkins, George W.
Date: December 7, 1900
Source: Source unknown; Cleveland Necrology File, Reel #012.
Notes: Calkins- On Tuesday, 7 p. m., at his residence, 43 Hough ave., George W. Calkins, age 77 years. Funeral from residence, Friday afternoon at 1 o'clock, standard time.

And their son's wife:
Name: Calkins, Harriet Trabue Stager
Date: April 24, 1892
Source: Source unknown; Cleveland Necrology File, Reel #012.
Notes: Calkins- At her residence, April 22nd, Harriet Trabue Stager, wife of Henry W. Calkins, in the 29th year of her age. Funeral services from 771 Bolton ave., Sunday, April 24th 1892, at 2 o'clock. Burial private.

=======================================

1815 - Arrived from Connecticut. Was the first school teacher in Brooklyn, Ohio.
1838 - County Commisioner in Brooklyn
1849 - Member of North Brooklyn Cemetery Association
1870 - Living in 12th ward / Farmer

Partner in the company, "Clarke, Graham, and White", manufacturers of pails, tubs, churns, and washboards.

His property was most likely in the area known as Ohio City.

MILITARY: Private in Company E, 54th Regiment

MARRIAGE:
AKIN, CAROLINE and CLARK, DIODATE vol.0002 pg.0030 (Cuyahoga County Marriage Index)
LINDSLEY, SALLY and CLARK, DEODATE vol.0002 pg.0178 (Cuyahoga County Marriage Index)

OBIT: Name: Clark, Diodate
Date: Sept. 9, 1878
Source: Cleveland Herald; Cleveland Necrology File, Reel #015.
Notes: Clark- September 4th, at 11 p. m. at his residence, 656 Columbus street, Diodate Clark, aged 78 years.

DEATH: Clark Diodata 9/4/1876 79 yr vol.1 pg.276
Note the discrepancy between this date and the one being used for his date of death. May have been a transcription error.
Source: Cuyahoga County Deaths 1867 - 1890Location: http://www.rootsweb.com/~ohcuyah2/deaths/coarch/part1/pg032.html

1. Tamison CLARK b. Abt 1824, Brooklyn, Cuyahoga, Ohio; d. 21 Jul 1856, Brooklyn Twp, Cuyahoga, Ohio.
2. Diodate CLARK b. 1825, Brooklyn, Cuyahoga, Ohio; d. Feb 1873, Cleveland, Cuyahoga, Ohio.

1. Sarah CLARK b. Abt 1831, Brooklyn, Cuyahoga, Ohio.
2. Harriet CLARK b. Abt 1836, Brooklyn, Cuyahoga, Ohio.
3. George CLARK b. Abt 1840, Brooklyn, Cuyahoga, Ohio.

1. Betsey Ann CLARK b. Abt 1812, ,, Connecticut.
2. Joseph CLARK
3. Carey CLARK
4. 1. Diodate CLARK b. 1800; d. 4 Sep 1878, Brooklyn, Cuyahoga, Ohio.
5. Mary CLARK
6. Phoebe CLARK b. 1790, Haddam, Middlesex, Connecticut; d. 1876, Painesville, Lake, Ohio.
7. Lydia CLARK
8. Hannah CLARK
9. Ruth CLARK
10. Maria CLARK