Nuclear reactors were a by-product of atomic bomb production — they were first invented and developed in order to produce plutonium, a fuel for nuclear weapons. Power-production from nuclear reactors lagged this by a decade or so.

Medical isotopes were the first "peaceful" application of the work of the atomic bomb, because they could be produced in bulk from — again — nuclear reactors. They were touted as the "peaceful" side of the atom, but for the first decade or so the balance of activity, output, and input was thoroughly on the side of the "warlike" side.

Even the eventual use of reactors for electricity generation came out of the military funding of the atom; the first practical power-reactor designs were for nuclear submarines, and were later adapted to civilian use.

So I would frame this less as "how did the military research help the peaceful research," and more "how did the civilian aspects develop as derivatives of the military research."