Lori, I found a few vital records re the family of John G. Gardner.
from RIGR-RI Vital Records New Series Esther A. Verry, of Elijah and Sarah A., b 6 Feb 1845 North Kingstown RI, d 13 Jan 1901 East Greenwich RI; married John G. Gardiner, son of George S., b 1841 East Greenwich; [The references cited for this information was Esther's East Greenwich death record and Central Falls marriage record 3:84.]
John G. Gardner b 1841 East Greenwich, son of George S. Gardner [source cited is CFm 3:84]
1850 census, Exeter RI George Gardner, 53 Hannah Gardner, 40 John G., 9 George A., 7 Warren L., 5
1860 census, West Greenwich RI The same family is recorded, 10 years older
1870 census, Providence RI John Gardner, 29 b RI, Carpenter wife Esther A., 25, b RI Emma G., 5 John F., 2 months
The father of John G. Gardner appears to be George Sweet Gardner b West Greenwich RI 26 May 1797 at West Greenwich, son of Samuel and Elizabeth Gardner.His birth is found in Arnold's VR of Rhode Island.The Hannah recorded as George's wife in 1850 and 1860 was either his 2nd or 3rd wife.
I found the following citation for one of the marriages in RIGR: George S. Gardiner, of Samuel, b Exeter May 1797, d East Greenwich 16 Nov 1863; buried in West Greenwich; married Molly/Polly Edwards, of Richard and Mary, b 24 Mar 1802, d 10 Jun 1828
There was also a marriage cited for a George S. Gardiner and Eliza Bateman 25 Feb 1836 [EGm 4:28] but nothing to indicate if this was the same George S. Gardiner.I found no mention of a marriage between George Gardiner and Hannah.