Having RFK along on the trip even saved JFK's life; JFK's adrenal disorder flared up, and he reached a temperature of 107 degrees, and for the second time in his life to that point, a priest gave JFK the Last Rites. RFK arranged for JFK to be taken to a US military hospital in Okinawa, which saved JFK's life. By the time JFK and RFK came back to the US, they had forged a bond that was very similar to that of Wilbur and Orville Wright.
JFK and RFK mapped out a strategy in which JFK would enter 10 Democratic state primaries, but they both knew which two primaries were the most important: Wisconsin and West Virginia. The Wisconsin primary was on 5 April 1960, and there seemed to be no natural fit for JFK in the state, given that JFK was moderate and Wisconsin was famously progressive. And, add Senator Hubert Humphrey from neighboring Minnesota to the mix, and most pundits expected JFK to simply skip Wisconsin and focus in Illinois. But as far as RFK was concerned, he had JFK positioned perfectly as the underdog; RFK told reporters that he had advised JFK to avoid Wisconsin, and many reporters believed him.
RFK activated the Kennedy campaign machinery that had merely been dormant, while Humphrey stitched together his campaign pretty much at the 11th Hour. Humphrey soon came to hate the reality that a campaign led by RFK didn't play fair; RFK let loose a rumor that Jimmy Hoffa was helping to finance Humphrey's campaign. Far more aggressively (using the "Low Road"), RFK authorized anti-Catholic information to be sent out in Wisconsin and simply blamed Humphrey for the mailings. The dirty work was conducted by Paul Corbin, who was in essence RFK's hatchetman, and RFK did absolutely nothing to stop him. JFK defeated Humphrey by 12 points, which wasn't quite the knockout blow that JFK and RFK had hoped for, and Humphrey was in high dudgeon after the primary (for some pretty good reasons).
JFK pushed every button that mattered to West Virginians, saying that his allegiance was to America, not the Pope, and reminding those in the state that FDR, Jr. was in his corner. West Virginia's crooked politics were a natural fit for JFK and RFK, since they had been trained in the brutal political arenas of Boston and Massachusetts. Humphrey attacked JFK's record in Congress, as well as his integrity, and, as JFK and RFK interpreted it, their religion. It reached the point where JFK and RFK decided to play really dirty, accusing Humphrey (with FDR Jr.'s help) of dodging the draft during World War II, which Humphrey simply didn't do (Humphrey had tried to enlist a few times, but for various reasons, he was denied).
Humphrey became apoplectic over the money the Kennedys had poured into West Virginia. While no one could prove it, prominent West Virginians and voting blocs were given the dreaded "Walking Around Money", which was campaign cash that wasn't "accounted for". In the end, the money wasn't the deciding factor, in that JFK defeated Humphrey 61% to 39%; that result ended the belief that a Catholic could not have national political appeal.
RFK was everywhere, putting out political brush fires set by LBJ, such as accusing JFK of being in very bad health, but LBJ was forced to eat crow since the Kennedy clan was able to keep JFK's Addison's Disease a secret. Although much was planned in advance, RFK had to think on his feet most of the time, applying the lessons he learned from the convention in 1956. RFK wanted an accurate assessment of where every convention delegate stood, and he did whatever he could (sometimes using tactics that J. Edgar Hoover would recognize) to convince as many delegates as possible to vote for his brother. JFK won on the first ballot, and LBJ was not able to steal the nomination; RFK knew that if JFK hadn't won the nomination on the first ballot, they were both sunk.
Theodore Sorensen (JFK's main speechwriter) and Joe both wanted LBJ, but RFK absolutely hated Johnson. For years, LBJ told the story how FDR had sacked Joe as the US Ambassador to Great Britain, and for those years RFK had been seething. The two men first met in 1953 in the Senate cafeteria when RFK was one of Senator Joseph McCarthy's lawyers. McCarthy and his retinue were eating when Johnson, the Senate Majority Leader, stopped by to say hello to McCarthy. Not only did RFK refuse to stand to shake the Senate Majority Leader's hand, he refused to make eye contact (LBJ wound up shaking RFK's hand sitting down). And then there was the deer hunting fiasco in Texas, which convinced RFK that LBJ was not only a bully, but also a brute. LBJ referred to RFK, to his face, as "Sonny Boy", and LBJ never tired of going after Joe; it seemed that the two were placed on Earth to bedevil the other.