I don't really think I can help you.John Dial Jr. (who married Nancy Wiley) was not born until 1781.How in the world did he fight in the Revolutionary War??It was John Dial (Dyal) Sr. who was the Rev soldier.He was married to Mary Todd.There must be some errors on those DAR papers you have.
Mary Etta Dyal was the daughter of George Washington Dyal and Maria Elizabeth Rooks -- check the census records in 1850 if you have doubts.Her father was not a William Washington Dyal as you have stated.
Mary Etta's daughter, Emma Florence married another George Washington Dyal who, I believe, was the son of James Nathaniel Dyal.(his mother Harriet was daughter of George Dial, son of John Dyal and Mary Todd.)So you do have a connection to John Dyal Sr on both sides.This is not my line so I have not documented it.
I, too, have the information concerning the Dyal line back to D'Oyley.Unfortunately, all of those family trees that show that information do not provide documentation. The only documentation you see is another tree with no documentation, and on and on it goes. Much of it was based on Hasting Harrison's work.
In his book "Martin Dial and Related Families" he states on page 210, "It is said by younger members of these families that they have proved to their satisfaction that their ancestor Thomas Dyall, the immigrant was a brother of my ancestor,Henry Arthur Dial,whose name may have been spelled as Dyal or Dyall in his youth. If their assumption is true, our families join in Isaac Malcolm and Harriett Blackwell Dyall of England."
Notice he said "If their assumption is true".I have not seen documentation for that connection yet, therefore I have not included them in my family file.I am in the process of acquiring his book to see what documentation he provides.There are so many errors in those online family trees.You need to always verify with actual records before accepting them as fact.
Have you seen actual records to document those generations?