AH Challenge: Kennedy Vs. Kennedy!

Currently, two brother are going up against each other for the leadership of the Labour Party in Great Britain. That got me wondering if it would be possible of something like the to happen in America with their most famous political family...

Your challenege, should you chose to accept it, is to have any two members of the Kennedy family go up against each other for the Demoratic Nomination for President. .You can chose the POD, but it must be no earlier than 1959. Bonus points if you can have it cross generational fight between father and son, or uncle and nephew.
 
Unfortunately this would be violating Family Rule #1: the family is a single unit, not subsets divided into various branches. The political PODs that prevented are innumerable.

LBJ's presidency goes better than OTL, he defeats Nixon in 1968 by a very narrow margin. RFK is re-elected over John Lindsay in 1970 with 68% of the vote and announces his 1972 candidacy in January 1971. They represent opposite wings of the party- Bobby what would later become the DLC faction, Ted the liberal, New Deal wing that had been in control from 1932 to 1971 (New Left takeover via McGovern-Fraser) and 1980 (DLC-er Carter's defeat) to 1985 (founding of the DLC) IOTL. Bobby wins and narrowly defeats Ronald Reagan in 1972. Reagan succeeds RFK in 1980, Ted succeeds Reagan in 1988.
 
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