Re: Rebecca Greene
Rebecca's birth and marriage occurred during the "dark period" for RI vital records. Very few vital records are available during this time in RI. So you need to find alternative sources.
The first place I suggest you look is for Rebecca's death record. If she died in RI in 1887, her death should have been recorded and it will list her parents, if the person providing the death information knew who they were.
You probably already have the census records:
Rebecca G. Jenks age 26, in 1850, b RI, was in Smithfield, Providence Co.
In 1860 Rebecca, 35, b RI, was in North Providence.
In 1870, Rebecca 48, b RI, was still in North Providence.
In 1880 Rebecca, 48, widow, b in RI, parents b RI, was living with her dau and son-in-law, in West Sprngfield, Hampden, MA.
So if you can't find Rebecca's death recorded in Smithfield, then look in Massachusetts.
I agree that David and Mary are unlikely to be Rebecca's parents.
In the 1850 census for Scituate there was only one Greene old enough to be Rebecca's parent. That was Sally Greene (incorrectly indexed by ancestry as Sawy). She was 76, b in RI. You could check the probate records for wills by people named Greene who named a dau Rebecca Jenks.