The energy landscape and its evolution with pressure have been studied for two hydroquinone clathrates in combination with the apohost beta-hydroquinone structure. Pressure is used as a means for probing interatomic, or intermolecular, potentials. The forces in organic clathrates are generally dominated by strong intermolecular interactions in a host framework, with smaller contributions from subtle interactions between the guest molecules and the surrounding framework. Pairwise intermolecular interactions energies have been quantified for the hydroquinone methanol and hydroquinone acetonitrile clathrate up to pressures of 8.6(2) and 14.1(4) GPa, respectively. In both cases, reversible pressure induced phase transitions are observed, where the host framework tilts to form skewed cavity channels and break the 3-fold rotation symmetry. The compression of the hydroquinone-acetonitrile structure is found to be isotropic, whereas it is anisotropic for the hydroquinone methanol compound, emphasizing the implication of different guest molecules. Host host interactions especially through the O-H---O bonding network have an order of magnitude larger contribution to the lattice energy than the host guest interactions, but these host-host interactions become increasingly less favorable with pressure ultimately leading the phase transitions. When small pressure is applied to the beta-hydroquinone apohost, it transforms to the denser a-hydroquinone structure. However, when guest atoms are enclathrated, a templating effect is observed leading to new and different high-pressure host structures. Thus, even though the host guest interactions are comparably modest in magnitude, the guest atoms direct the, high-pressure structural rearrangements. The present study illustrates the complexity of the numerous superimposed interactions in even the simplest supramolecular aggregates, highlighting the need to reliably quantify intermolecular interaction energies before aspiring to predict the formation of more complex supramolecular structures.