Investigations of shock-induced cavitation within a droplet is highly challenged by the multiphase nature of the mechanisms involved. Within the context of heterogeneous nucleation, we introduce a thermodynamically well-posed multiphase numerical model accounting for phase compression and expansion, which relies on a finite pressure-relaxation rate formulation. We simulate (i) the spherical collapse of a bubble in a free field, (ii) the interaction of a cylindrical water droplet with a planar shock wave, and (iii) the high-speed impact of a gelatin droplet onto a solid surface. The determination of the finite pressure-relaxation rate is done by comparing the numerical results with the Keller-Miksis model, and the corresponding experiments of Sembian et al. and Field, Dear, and Ogren, respectively. For the latter two, the pressure-relaxation rate is found to be µ = 3.5 and µ = 0.5, respectively. Upon validation of the determined pressure-relaxation rate, we run parametric simulations to elucidate the critical Mach number from which cavitation is likely to occur. Complementing simulations with a geometrical acoustic model, we provide a phenomenological description of the shock-induced cavitation within a droplet, as well as a discussion on the bubble-cloud growth effect on the droplet flow field. The usual prediction of the bubble cloud center, given in the literature, is eventually modified to account for the expansion wave magnitude.