Plausible scenario (at least in terms of big ideas) but I would replace RFK with Ted Kennedy. Robert Kennedy in an alternate world would probably be less willing to be an elected politician so much as a managerial figure for the Kennedy dynasty. Although others may disagree, and perhaps fairly. OTL Robert Kennedy stepped into electoral politics to carry a mantle for a slain brother, and after serving in appointed office. I think carrying a mantle would be much different if it were just JFK losing. I think the next logical step is JFK winning 1968 (#nosuperaddisontrope) or Teddy running. Teddy was a natural politician, even in ways John Kennedy was not. Robert Kennedy had a hard time being a politician. I think it would be Ted Kennedy as run by Robert Kennedy, with RFK and JFK serving in support roles; JFK more openly, and RFK more as a shadow figure. That gets more complicated by JFK remaining in his Senate seat. Maybe Ted works his way to congressmen or governor or something. Or maybe he goes to another state, as RFK did.
Anyway, Westmoreland certainly thought he would be president. As did many people who knew him. The biggest problem with Westmoreland is his ego. He had a giant self confidence, and refused to accept blame. He was certain that what he wanted to work would work, and was working. And that is the big problem with his handling of the Vietnam War. If the data did not support his position and policies, the data was wrong, and it would need to be corrected to show just how much he was surely succeeding. And I expect nothing different in a presidency. He'd have a Reagan posturing and shaping of narrative and context, but without the Reagan charisma to sell it as far as he would need to.
Also, here's a presidential looking image.