There remains a gap in our knowledge of the fundamental physical determinants of dynamical interactions between the constituents of two-dimensional hybrid perovskites, sometimes called self-assembled quantum wells (SAQWs). In this study, we use the anharmonic properties of vibrations localized on the molecular cations of two separate SAQW samples to characterize their coupling to low-frequency phonons in these materials. For the case of an aromatic molecular cation, benzyl ammonium, we use analysis of Raman spectra to propose that the quartic anharmonic coupling to phonons spread over both the organic and inorganic sublattices explains the spectral position of its ammonium bending vibration as a function of temperature. In contrast, we find that the cubic anharmonic coupling to phonons of the inorganic octahedral layers qualitatively explains the temperature-dependent peak position of this vibration for an alkyl molecular cation, hexyl ammonium. Furthermore, we use density functional theory calculations to construct the two-vibration density of states and characterize how cubic anharmonic coupling explains the shape of the ammonium bending vibrational peak in each material. Using this method, we explain the asymmetric shape of the NH3+ bending peak in hexyl ammonium lead iodide when measured at room temperature. Our results provide fundamental physical insights into the dynamical interactions between the organic and inorganic constituents of hybrid SAQWs necessary to further develop their use in thermal, mechanical, and electronic technologies.