I have a book called The Lisle Letters, which is an abridged copy of a 3-volume set of Lord Lisle’s letters. Lord Lisle was a one of the last surviving fairly direct Platagenets, only a little bit illegitimate. As a result, Henry VII’s spies kept very close tabs on him, eventually arresting him for suspected treason; he was kept in the Tower and had a heart attack when told he was being released. In the process of keeping tabs on him, and after his arrest, they collected enough of his personal correspondence to fill 3 volumes.
Henry VII and VIII were well aware that they had a less-than-sterling claim to the throne. As the Lady Jane Grey episode (much) later demonstrated, any faction that wanted power need only find a valid figurehead to stand behind to give their cause legitimacy, even if that person themselves harboured no great ambition. As a result, a lot of the Tudor activity was keeping stiflingly serious tabs on any potential rivals and preventing them from getting too friendly with rival factions.
If Henry makes his agreement to marry Elizabeth in December of 1483, it must mean that the Yorkists knew by that time that the Edward V and the Duke were dead.
Incidentally, Elizabeth Woodville, the mother of Elizabeth of York and Edward IV’s wife/concubine (if you believe Richard III) lost her three sons, her brother and her husband within a space of one year. The poor woman must have gone mad.
Henry VIII OTH adored his mother. Even in his old age he continued to be moved to tears recollecting her death.
I do wonder what would have happened if she had still been alive come the whole Anne Boleyn issue came about, she might have been able to restrain Henry.