There is John Gladding who was one of the original settlers of Newbury MA. I don't know about any Gladden in Plymouth, maybe they mean the one in Newbury. There is a First Families of Newbury and John Gladding is listed. He married Elizabeth Rogers and gave his age as 37 when he took oath of allegiance in 1678. No one knows where or when he was born but it's estimated at 1641 in England.
They left MA after the Indian Wars and he was the first settler of Bristol RI. There were many children and many became prosperous and well known. There is a Gladding House in Bristol and there are portraits in the Historical Society.
There has been much speculation about the youngest son, Joshua, much confusion about his name and whether he was three different people! Confusing due to lack of information. A professional genealogist settled the matter in an article in The American Genealogist (: Janet Ireland Delorey, "Revisiting John^1 Gladding of Newbury, Massachusetts and Bristol, Rhode Island," The American Genealogist, 77 (July 2002, October 2002): .
She answered my query as to the probability that this John Gladding is the father of the Joshua Gladding in Saybrook CT who was The Blacksmith. She told me that there is no PROOF but there is enough circumstantial evidence that they are the same person My family apparently comes from this Joshua although I have a brick wall as to whether his son Joshua was the father of my Azariah Gladding.
As to the mentioned Washington Gladden, he comes from this same line and is related to me. He lived in Easthampton MA and is buried in Northampton, I think. I saw his gravestone, I think it was Northampton. He was a minister and wrote for the Springfield MA newspapers. He did not know for certain (just as we do not know) whether he was related to the Gladdings of Bristol RI.
There is a old Gladding Book that is wrong in many places. We need to know more about the Gladding/Gladden family, in particular, the descendants of Joshua who went to Connecticut. The family members who remained in Rhode Island are well documented and one of their descendants is Geo. Bush.