We investigate "negative-ion-to-neutral-to-positive-ion" (NENEPO) pump-probe spectroscopy as proposed by Wt;ste and co-workers [Wolf et al., Phys. Rev. Lett. 74, 4177 (1995)] where the dynamics of wave packets in a neutral molecule produced by photodetachment from the negative ion is probed by time-delayed photoionization and detection of positive molecular ions or photoelectrons. Approximations are introduced for an effective numerical treatment of the double-ionization process. The organometallic compound FeCO is used as an example.