I can not connect Abby Churchill, General Sylvester's niece, to any of his brothers. The publication,( Churchill Family in America ), does not list her as a child of any of the brothers. Do you know which one was her father?
General Sylvester Churchill 1783-1862 was a direct CFA descendent of John Churchill and Hannah Pontus of the Plymouth Colony in the mid-1600s. - Sylvester, Joseph, Joseph, Barnabas, Joseph, to John & Hannah.
I am not aware of any relationship of Sir Winston Leonard Spencer-Churchill, the wartime Prime Minister of England, to North American Churchills. There may well be one, but it would likely have to be through his mother Jennie Jerome.
Sir Winston's direct CFA line is the Spencer line. The 5th. Duke of Marlborough, George Spencer b. 1766 petioned the Crown to add Churchill as a second surname. This was done for financial reasons related to the Dukedom of Marlborough. One would have to go back 7 generations from Winston to Lady Ann B Churchill, the 2nd Duchess of Marlborough who married George Spencer. They would have been his 5th. great grandparents, Lady Anne being the first actual Churchill connection. She was the daughter of John Churchill the 1st. Duke of Marlborough. Her husband, George Spencer, became the 2nd. Duke as John Churchill, the first Duke, had died without any surviving male children. This Dukedom is still today the only dukedom that can pass to a female heir.