Probably not; Joe Jr. had already completed two tours of duty flying Liberator bombers prior to the mission that killed him. If Jack had been killed he’d have been very unlikely to have served more than one tour. And if Joe Jr. is killed, there is still Bobby Kennedy; Joe Sr. was going to make sure one of his boys reached the White House.
I agree-if JFK dies, the "mantel" will pass to Robert, assuming the butterflies don't ensure his older brother's survival.
If RFK beats lodge in 58, Nixon may not pick him for VP 2 years later-the loss being only a couple of years before the election. That could well mean Ford runs with Nixon-if he excepts. LBJ probably gets the Dem nomination, with Humphrey as his running mate. If this happens, Nixon probably wins a very close, 2000 style election.
Nixon being in office will probably prevent the Cuban Missile Crisis. I imagine Nixon pushes for Civel Rights and gets a substancial package through congress, but as others have said, he'll have more difficulty than LBJ did in OTL.
I don't think Oswald shoots Nixon-for starters, Nixon's schedule will be different to JFK's in OTL and he won't be visiting Dalace on that day-and he won't have the same political reasons for doing so.
Another thing that won't be happenning is any watergate-esc revilations. That's not to say their won't be anything resembling Watergate in the runup to the 64 elections, but it won't be on the same scail and it's not likely to be revealed in public, at least not until after his presidency.
I believe that Nixon probably wins reelection in 1964, though that's by no means certain. Bobby probably won't run unless Nixon seems particularly vunnerable, as 68 (which is only 4 years away) will be an open race. Don't know who the candidates will be though. Humphrey maybe? Scoop Jackson is a possibility.
If we assume Nixon wins in 64, then the Democratic nominee in 68 is almost guarantied to become the next president.