Elfwine said:
Margaret would sooner take poison than marry her daughter to the spawn of York.
The two parties have too many quarrels between them for this to be acceptable.
Well, that was only a supposition. I was actually more looking for a scenario where York would force Margaret of Anjou's hand. However, given how Henry VI's queen acted during the Roses' War, she will probably do anything to escape York's hands and thus such a situation.
Elfwine said:
Also, I'm not sure if they're close enough to need a dispensation. The two houses are cousins, but I'm not sure how close (and how close is too close).
The Lancaster and York are both descendants of Edward III: the Lancaster are scions of John of Gaunt, Edward III's third son, while the York have blood from both Edward III's second and fourth son, Lionel of Clarence and Edmund of York.
Technically, the Catholic Church forbade marriage within the fourth degree of consanguinity: the two spouses thus mustn't have at least one great great great grandfather in common. I'm pretty sure there was no intermarriage between the Yorks and Lancaster between Edward III and the situation we're discussing. Thus, Edward III is the closest common ancestor of the two houses.
To Henry VI, Edward III is great great grandfather. Thus, he is a great great great grandfather of his daughter in the scenario we're discussing.
To Edward IV, Edward III is a great great grandfather via Edmund of York and a great great great great grandfather via Lionel of Clarence.
Thus Edward IV would be a 4th cousin 1ce Removed of Henry VI's daughter via his descent from Edmund of York while he would be a 5th cousin 1ce Removed via his descent from Lionel of Clarence. In other words, they are not too closely related and wouldn't require a dispence from the Pope.
But even if they had been in forbidden degree of consanguinity, papal dispency wasn't a problem: the Popes were generally concilient in regards to dynastic marriages.
For example, Edward I's second wife was Margaret of France, half sister of Philip IV. They were related because Edward I's father, Henry III, had married the sister of Margaret of Provence, queen of Louis IX of France. Thus, to Edward I, his second wife was a 1st cousin 1ce Removed. The Pope gave his consent without thinking twice despite consanguinity. He also didn't give any objection to Edward II and Isabelle of France who were 2nd cousins 1ce Removed.