Actually, I always got the impression the main reason Michael objected was because they were first cousins. I'm not as "in the know" about GFIII as the first two, but I could swear Michael made the "cousin" reference to Vincent, showing his objection.
TIS
"Mankind must put an end to war before war puts an end to mankind. War will exist until that distant day when the conscientious objector enjoys the same reputation and prestige that the warrior does today." JFK