We present a set of four Gemini-North Multi-Object Spectrograph/integral field unit (IFU) observations of the central disturbed regions of the dwarf irregular starburst galaxy NGC 1569, surrounding the well-known superstar clusters A and B. This continues on directly from a companion paper, in which we describe the data reduction and analysis techniques employed and present the analysis of one of the IFU pointings. By decomposing the emission-line profiles across the IFU fields, we map out the properties of each individual component identified and identify a number of relationships and correlations that allow us to investigate in detail the state of the ionized interstellar medium (ISM). Our observations support and expand on the main findings from the analysis of the first IFU position, where we conclude that a broad (<~400 kms-1) component underlying the bright nebular emission lines is produced in a turbulent mixing layer on the surface of cool gas knots, set up by the impact of the fast-flowing cluster winds. We discuss the kinematic, electron-density and excitation maps of each region in detail and compare our results to previous studies. Our analysis reveals a very complex environment with many overlapping and superimposed components, including dissolving gas knots, rapidly expanding shocked shells and embedded ionizing sources, but no evidence for organized bulk motions. We conclude that the four IFU positions presented here lie well within the starburst region where energy is injected, and, from the lack of substantial ordered gas flows, within the quasi-hydrostatic zone of the wind interior to the sonic point. The net outflow occurs at radii beyond 100-200 pc, but our data imply that mass-loading of the hot ISM is active even at the roots of the wind.