This article examines the combined effect of plasma rotation, magnetic field, and several parameters on the dust-ion-acoustic solitary waves (DIASWs). A rotating plasma system is assumed that comprises positive ions (mobile and adiabatic), negative light ions (trapped), isothermal electrons, and dust particles (stationary and positively or negatively charged). Using the reductive perturbation technique (RPT), the mKdV equation is obtained to investigate the variations in wave nature caused by different forces and parameters. It is found that the external magnetic field, oblique rotation, electron and dust concentrations play a key role in varying wave amplitude, width as well as phase speed. Depending on whether the dust is positively or negatively charged, the rotational frequency increases (decreases) the phase speed (amplitude and width). Moreover, the magnetic field enhances the wave amplitude but reduces the width. The results obtained from the study are expected to be useful in describing rotating flows of magnetized plasmas observed in white dwarfs, neutron stars, pulsar radiations, etc.