I don't see much changing, because he was almost never at the WH IOTL, and both brothers didn't really want him interfering. RFK was his deputy, and sometimes used executive authority in JFK's name when he was ill or things arose. One thing Joe could've prevented was the Manchester book scandal- relatively minor, but cost Bobby fifteen points in popularity, the lead over Johnson for the '68 nomination (those polls were published beginning in mid '66) and the polarity numbers, which then were as bad or worse than the SecState. Only for a few months though. As I said, it won't really affect the JFK Presidency.