You are right about the Plantagenets. I discovered I was a descendant of Thomas Dudley, the first governor of Massachusetts Bay Colony, who in turn was a descendant of Henry II, a Plantagenet king. Secretary of State John Kerry is also a descendant of Thomas Dudley, a relation I am not exactly proud to admit.
And you are right about the Tudors, easily the most bloody dynasty ever to rule England, although they did succeed in making Great Beitain a dominant European colonial and super power of that age.
When Elizabeth I was crowned, England was a nation of a mere 2.5 million who had lost all their overseas possessions under the incompetent rule of her father and her sister Mary. It is estimated that 72,000 English were executed under the reign of Henry VIII, roughly 3% of the entire population, mostly for political and petty crimes.
I would suspect that your same Dudley line is a branch of the same family who was terminated with the brutal execution of Lady Jane Grey and her husband by orders of Mary I.
In 20-20 hindsight, it is easy to see why the American Revolution was inevitable with bad blood between the ruling class and those they ruled dating back nearly three centuries before the revolution in the old country.