We have measured the evolution with depth z of the vicinage effect and Coulomb explosion for H-2(+) and H-3(+) molecular ions traversing thick, uniform amorphous targets of Si3N4 and SiO2. High depth resolution is achieved by scanning the energy per nucleus of the incoming molecules E-b around the energy E-R corresponding to narrow resonances in the cross sections of O-18(p, alpha)N-15 at 151 keV and in N-15(p, alpha gamma)C-12 at 429 keV. The corresponding reaction yield Y (E-b) is, to first order, inversely proportional to the stopping force S-mol on the molecular fragments, giving a direct image of the evolution of the vicinage effect and Coulomb explosion with z. At the target surface, the vicinage effect enhances the stopping force on the molecules by a factor chi > 1. As they penetrate the matter, the distance between the molecule nuclei increases, as a consequence of Coulomb explosion and multiple scattering lateral displacement, and the vicinage effect decreases with depth z. The experiment yields information on the screened Coulomb repulsive potential via the repulsion velocity V-lim observed at large z, where the distances R-ij between the molecule nuclei are large compared to the adiabatic cutoff R-ad (no vicinage effect). We show that the first order view, that Y (Eb) proportional to S-mol(-1), is profoundly modified by the energy fluctuations induced by the Coulomb explosion and lateral multiple scattering. Our observations are satisfactorily reproduced when modeled using a dynamic screening radius r(s) in the range R-ad (for H-3(+)) to 2R(ad) (for H-2(+)) for the Coulomb explosion and the evolution with R-ij of chi given by the dielectric model for the interaction of the exploding molecules with the target electron gas.