Hi Rick! you have a very interesting situation there! Looks like that is the very transition from the Welsh patronymics to the English surnames. The children Robert, Katherine and Elizabeth use the surname Williams because their father's first name was William. They are firmly on the patronymic system. Robert's children have shifted over to the English surname system, using Williams as their family name right down to the present time.
Apparently Robert, Katherine and Elizabeth's father's name was William and he was the son of Edward -- that is why the memorial inscription says William ap Edward. You have grasped all this, according to your question, but now your challenge is to help the other Profile Managers understand it -- is that what is going on?