Global instabilities in swirling flows can significantly alter the flame and flow dynamics of swirl-stabilized flames, such as those in modern gas turbine engines. In this study, we characterize the interaction between the precessing vortex core (PVC), which is the consequence of a global hydrodynamic instability, and thermoacoustic instabilities, which are the result of a coupling between combustor acoustics and the unsteady heat release rate. This study is performed using experimental data obtained from a model gas turbine combustor employing two concentric swirling nozzles of air, separated by a ring of fuel injectors, operating at five bar pressure. The flow split between the two streams is systematically varied to observe the impact of flow structure variation on the system dynamics at both non-reacting and reacting conditions. High-speed stereoscopic particle image velocimetry, OH planar laser-induced fluorescence and acetone planar laser-induced fluorescence are used to obtain information about the velocity fields, flame and fuel flow behaviour, respectively. Spectral proper orthogonal decomposition and a complex network analysis are used to identify and characterize the dominant oscillation mechanisms driving the system. In the non-reacting data, a PVC is present in most cases and the amplitude of the oscillation increases with increasing flow through the centre nozzle. In the reacting data, three dominant modes are seen: two thermoacoustic modes and the PVC. Our results show that in the cases where the frequency of the PVC overlaps with either of the thermoacoustic modes, the thermoacoustic modes are suppressed. The complex network analysis coupled with a weakly nonlinear theoretical analysis suggests the mechanisms by which this coupling and suppression of the thermoacoustic mode occur.