The HIV-1 capsid is an irregularly shaped complex of about 1200 protein chains containing the viral genome and several viral proteins. Together, these components are the key to unlocking passage into the nucleus, allowing for permanent integration of the viral genome into the host cell genome. Recent interest into the role of the capsid in viral replication has been driven by the approval of the first-in-class drug lenacapavir, which marks the first drug approved to target a non-enzymatic HIV-1 viral protein. In addition to lenacapavir, other small molecules such as the drug-like compound PF74, and the anionic sugar inositolhexakisphosphate (IP6), are known to impact capsid stability, and although this is widely accepted as a therapeutic effect, the mechanisms through which they do so remain unknown. In this study, we employed a systematic atomistic simulation approach to study the impact of molecules bound to hexamers at the central pore (IP6) and the FG-binding site (PF74) on capsid oligomer dynamics, compared to apo hexamers and pentamers. We found that neither small molecule had a sizeable impact on the free energy of binding of the interface between neighboring hexamers but that both had impacts on the free energy profiles of performing angular deformations to the pair of oligomers akin to the variations in curvature along the irregular surface of the capsid. The IP6 cofactor, on one hand, stabilizes a pair of neighboring hexamers in their flattest configurations, whereas without IP6, the hexamers prefer a high tilt angle between them. On the other hand, having PF74 bound introduces a strong preference for intermediate tilt angles. These results suggest that structural instability is a natural feature of the HIV-1 capsid which is modulated by molecules bound in either the central pore or the FG-binding site. Such modulators, despite sharing many of the same effects on non-bonded interactions at the various protein-protein interfaces, have decidedly different effects on the flexibility of the complex. This study provides a detailed model of the HIV-1 capsid and its interactions with small molecules, informing structure-based drug design, as well as experimental design and interpretation.