We report on Herschel/PACS observations of absorption lines of OH⁺, H₂O⁺ and H₃O⁺ in NGC 4418 and Arp 220. Excited lines of OH⁺ and H₂O⁺ with E_lower of at least 285 and ~200 K, respectively, are detected in both sources, indicating radiative pumping and location in the high radiation density environment of the nuclear regions. Abundance ratios OH⁺/H₂O⁺ of 1−2.5 are estimated in the nuclei of both sources. The inferred OH⁺ column and abundance relative to H nuclei are (0.5−1) × 10¹⁶ cm^-2 and ~ 2 × 10^-8, respectively. Additionally, in Arp 220, an extended low excitation component around the nuclear region is found to have OH⁺/H₂O⁺ ~ 5−10. H₃O⁺ is detected in both sources with N(H₃O⁺) ~ (0.5−2) × 10¹⁶ cm^-2, and in Arp 220 the pure inversion, metastable lines indicate a high rotational temperature of ~500 K, indicative of formation pumping and/or hot gas. Simple chemical models favor an ionization sequence dominated by H⁺ → O⁺ → OH⁺ → H₂O⁺ → H₃O⁺, and we also argue that the H⁺ production is most likely dominated by X-ray/cosmic ray ionization. The full set of observations and models leads us to propose that the molecular ions arise in a relatively low density (≳10⁴ cm^-3) interclump medium, in which case the ionization rate per H nucleus (including secondary ionizations) is ζ > 10^-13 s^-1, a lower limit that is several × 10² times the highest current rate estimates for Galactic regions. In Arp 220, our lower limit for ζ is compatible with estimates for the cosmic ray energy density inferred previously from the supernova rate and synchrotron radio emission, and also with the expected ionization rate produced by X-rays. In NGC 4418, we argue that X-ray ionization due to an active galactic nucleus is responsible for the molecular ion production.