You have all three of the Kennedy Brothers in reserve for the late 60s, 70s and 80s. None of them will be assassinated.
As for what HHH will do, I would expect Humphrey to have at least as good a chance as Kennedy of winning the 1960 election. And passing Civil Rights legislation, since he will be equally beholden to Northern African-American voters.
Will he make JFK or LBJ his running mate? Hard to say? Probably LBJ. HHH would need Texas as much as Kennedy would and he would want Johnson's political skills in his corner.
As far as Cuba is concerned, I think Humphrey would be more inclined than Kennedy to back the CIA up on Bay of Pigs. Scratch Fidel Castro.
Would this make Humphrey more or less inclined to go to the mattresses in South Vietnam?
Perhaps less, if the dominos had already been stopped by Suharto's coup in Indonesia and Humphrey already had proven his anti-Communist chops by overthrowing Castro.
But if Humphrey DID intervene in Vietnam, it would be a lot earlier--in 1961 or 1962 --over Laos.
Remember the Laos Crisis?
IOTL, North Vietnam's opening move in taking over South Vietnam was to attempt to take over Laos. Kennedy attempted to block the North Vietnamese with covert aid to the Laotian Royalists. In 1962, a negotiated settlement was reached that left a neutralist government in power but in reality left Laos divided lengthwise with the Communists in control of the eastern half of Laos in which they could set up the Ho Chi Minh Trail.
I suspect that Humphrey rather than accept a neutrlaist fig leaf as Kennedy did, might have chosen to escalate Laos immediately and invade Southern North Vietnam, stopping at the River Ca at Thanh Hoa. This would be a position that would be hopefully non-threatening to China and avoid a Chinese counter-attack (ala Korea) yet be defensible (or enable a retreat to a defensible line) if China did come to North Vietnam's rescue. The attack would then continue over Barthelemy Pass to a defensive line including Xieng Khouang on the Plain of Jars (but not including Sam Neua, holding Vientiane and Luang Prabang and holding Nam Tha (but not all of Nam Tha Province and finally reaching the Mekong on the Burmese border. And it would be on this line that Communism would be contained from Vietnam, Laos, Cambodia and Thailand.
How much more succesful an intervention might be at this juncture I don't know. A defensive line across Northern Laos would certainly keep the North Vietnamese away from populated areas in South Vietnam and might well strangle the Viet Cong in it's cradle. It would not make the problems of the South Vietnamese government go away, however, or decrease the alienation of the South Vietnamese people from that government. And the US would be involved in "pacifying" occupied annexed to South Vietnam, Southern North Vietnam, places like Dong Hoi, Vinh and Thanh Hoa.
The estimates were for 60,000 troops for Laos alone. I would suspect 150,000 US troops for this intervention for an indeterminate length of time, a lot sooner and becoming an issue in the 1964 election before it became an issue in the 1968 election. I think Humphrey, while more of a liberal on civil rights than Kennedy, would definitely have been more of a hawk on Indochina a lot sooner.
