When a core-shell electron is ionized by coherent ultrashort x-ray pulses with varied duration, different nuclear wave packets of a cationic molecule are formed, which can be effectively studied by detecting the photoelectron -Auger electron-ion fragment as it is proposed in the present paper. We develop the theory for the photoelectron, i.e., Auger electron, ion fragment three-body coincidence spectroscopy, where dissociative Auger final states are considered. Simulations to display the HF molecule show that the coincidence spectra encode the detailed information of coherent nuclear wave-packet dynamics. Our work paves the way for using currently available coherent ultrashort x-ray pulses to investigate and manipulate molecular nuclear wave packets. Moreover, we discuss possibilities for high-resolution coincidence experimental techniques.