IOTL, between WWII and about 1960 there was an extended debate on which military service ballistic missiles ought to "belong to" in terms of procuring, maintaining, and operating these vehicles. This was largely between the Army (ballistic missiles as very long range artillery) and the Air Force (they go through space, man, and space is like...above the atmosphere and stuff!). The Air Force ended up "winning" the debate IOTL, which had a lot of later unintended consequences, mainly on the space program.
However, this was far from preordained. The Army's claim that ballistic missiles are basically just really, really long range artillery makes more sense (when you get down to it) than the Air Force's rather incoherent reasons for giving them control. More importantly, the Army until 1958 had the services of what was undoubtedly the most experienced ballistic missile design team in the world, namely von Braun et. al. So...suppose that things go the other way. Maybe Eisenhower remembers being an Army man, or perhaps he acts out of a desire to balance the military's nuclear delivery systems (Navy bombers, Air Force strategic bombers, and Army missiles). In any case, the Army, not the Air Force, is responsible for R&D on ICBMs, IRBMs, and other types of ballistic missile (except for SLBMs, which as per OTL become Navy-controlled, probably with less fuss). What happens?
However, this was far from preordained. The Army's claim that ballistic missiles are basically just really, really long range artillery makes more sense (when you get down to it) than the Air Force's rather incoherent reasons for giving them control. More importantly, the Army until 1958 had the services of what was undoubtedly the most experienced ballistic missile design team in the world, namely von Braun et. al. So...suppose that things go the other way. Maybe Eisenhower remembers being an Army man, or perhaps he acts out of a desire to balance the military's nuclear delivery systems (Navy bombers, Air Force strategic bombers, and Army missiles). In any case, the Army, not the Air Force, is responsible for R&D on ICBMs, IRBMs, and other types of ballistic missile (except for SLBMs, which as per OTL become Navy-controlled, probably with less fuss). What happens?