George Tudor, Duke of York and Somerset

If Henry VII's son had lived long enough to produce a boy (lets call him George) with Ursula Pole in say 1520 and dies before producing a second child. How would the young Duke of York and Somerset be seen by the court? Would Henry marry him to his daughter? Would this boy's birth save the Pole family? Or would he be executed along with them?
 
If Henry VII's son had lived long enough to produce a boy (lets call him George) with Ursula Pole in say 1520 and dies before producing a second child. How would the young Duke of York and Somerset be seen by the court? Would Henry marry him to his daughter? Would this boy's birth save the Pole family? Or would he be executed along with them?

I'm confused, which of Henry VII's sons is this?
 
Edmund, Duke of Somerset is unlikely to be granted the title Duke of York as well as Duke of Somerset. York was a royal title somewhat associated with the second son, but unlike other monarchies, at the time England had no set system for titling the children, just a bunch of available titles.
 
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