The disparity in cost between manned and unmanned in OTL is what set the technology path we went on. While the distrust did exist, something like Corona would have happened because it was a great advantage over U-2 overflights. And considerably cheaper than trying to get people up there. Perhaps it would been delayed a few years but the consequence would have been no space reconnaissance not a shift into manned military flight.
If you read Dark Sun and other books on the design of nuclear warhead the miniaturization was develop from a breakthrough by Stanislaw Ulam. They would have figured it out someday but Ulam figured out it early enough that effected the design of the first generation of ICBMs. In short it was a bit of a relief as the payload could be made a lot smaller than the original estimates.
If Ulam had died in a car accident or something similar then the miniaturization technology would not have been developed as soon which would have meant that the early ICBM would be designed to launch a much bigger payload. Which would meant that the US could have match Soviet stunts much sooner and launched ambitious projects in the early sixties instead of having to wait until the mid 60s to launch large payloads.
You mentioned that Eisenhower distrusted the CIA. Eisenhower was also budget conscious and only support project to extent to what he felt was to be a national goal. So he would not have supported the development of large payload ICBM (which you need for spaceplanes) unless there was reason to do so. Heavyweight Nuclear Warheads would have provided such a reason. In addition with the reconnaissance that was being done from all sources. A true picture of Soviet nuclear capability emerged Esinhower realized that the US was far far ahead. Thus lessening the need for expensive measures.
The Altas were marginal in their ability to launch manned spacecraft. A consequence of the early successful miniaturization of spacecraft. The US could not match Soviet space efforts until the mid 60s when the Titans came available. Earlier Titans did not have payload need to do anything consequential for manned space. Dynasoar was paced by the need to fit it on the available boosters. With larger payload rockets more could have done sooner and hopefully before McNamara got his finger in and kill Dynasoar.
I suspect that we agree more than we disagree...
Corona was absolutely going to happen anyway, but without Eisenhower's almost pathological (and somewhat justified) distrust of the CIA, it likely would have ended up as a 'nice to have' rather than a central focus that tended to draw everything else in. By 1957/58, virtually everything being done in booster development was being done with Corona in mind, with disastrous results for almost everything OTHER than Corona. If we assume that Corona was just one priority among many, it isn't too hard to imagine several different approaches to the problem (different sized boosters, different technical approaches to manned space, automation, etc.) being approached. Just as JFK's Apollo focus left every other method of getting into space subordinated to Apollo (thus killing numerous programs with great promise), Corona did the same thing in the 1950s.
While there is no question that Corona was cheaper than manned space, it was also FAR more expensive than U-2s, and far less capable in many ways. Corona couldn't provide time sensitive intelligence, was very limited in terms of SIGINT and dust collection - essential for nuclear testing monitoring - and was also (largely as a result of the state of launcher technology) far less reliable in general. There is a reason that the U-2 survived (and in the guise of the TR-1 and follow-ons, still survives) for such a long time. It can be argued (and was argued) that a manned space/U-2 mix would give better strategic intelligence than would Corona, but it ran into the Eisenhower distrust of the CIA every time.
I have indeed read Dark Sun (the last book in the series is due out shortly, as I understand it), and found the discussion of Ulam interesting. My father knew Ulam reasonably well, and loved to tell stories about his propensity for practical jokes, but that is another story... To return to your point, however, Ulam's breakthrough was essential, but the lack of it might have simply meant that the US pursued manned bombers for longer than in our time line. Big boosters were a very serious problem for the US early on, largely because of issues with fueling. It doesn't strike me as especially likely that this was going to be sped up a great deal (the empahsis on ICBM development in OTL was already pretty much maxing out the technical talent available), and bombers were (comparatively) cheaper and easier to build at the time. I am not suggesting that your scenario is possible, only that it is somewhat less likely than that of simply pursuing manned aircraft (B-70, anyone?) for a bit longer while ICBMs caught up.
I am not entirely sure that I share your assessment that a big booster is necessary for a spaceplane. For a DynaSoar, you absolutely need a fairly capable vehicle, but an early model spaceplane (fewer passengers, etc.) is far less demanding. More to the point, however, smaller boosters could easily handle capsules (the Atlas had a significant payload margin for the Mercury, for instance, and could have handled any one of the various MISS designs that were circulating in the mid to late 1950s), and something the size of a DynaSoar wouldn't be ready before the bigger boosters were online in any case. As a side point, I believe that spaceplanes would have eventually ended up as a solution for personnel transport (though not for cargo, this is the biggest design flaw in the shuttle), but there are plenty of excellent capsule-centric approaches as well. The Gemini spacecraft was far superior to the Apollo, for instance, and Big Gemini would have been better still. The advantage of smaller boosters in this sense is that payloads would have been broken up, and we might have ended up with cargo rockets (much simpler and easier...and cheaper...to build) for bulk payloads with spaceplanes, capsules, and other low margin vehicles for people. As my liberal friends like to say...DIVERSITY!