Think the problem is that there were a number of John Pleasantons. The information that I have has been passed down through several generations. It goes like this: John Pleasanton married Widow Lester around 1720. They had 5 children_ Johathon, David, John, Mary and Deborah. David married Deboradh Luff around 1755-60. They had 4 children John and Sarah were two of them. Unfortunately I do not have names for the other two. Perhaps your Nathaniel was one of them. John married Susanna Stevens and Sarah married Outten Laws. The Laws had one child, Deborah who married William Heverin. This is the line through which I decend.
My records do not show any Nathaniel Pleasanton or Margaret White. However the name "Nathaniel" is found frequently in the Luff family line. Sorry that I can't be more helpful. Know nothing about General Alfred Pleasanton.