A common ancestor could be claimed by all of the major players in the Wars of the Roses.
Not just the men leading on the battlefield, but their wives waiting at home, could generally trace their lineage back to Edward III. It was his grandchildren who caused all of the trouble, and it would take several generations to bring those branches back together.
Securing the throne, and peace in Britain, led to a lot of interbreeding within the House of Plantagenet. It eventually worked, but then, it had created the conflict in the first place!