The orthorhombic Pca21 phase of HfO2 exhibits exceptional ferroelectric stability at the nanoscale, yet its intrinsically high coercive field Ec remains a significant obstacle to practical applications. The recent discovery of an interstitially doped ferroelectric rhombohedral R3m phase in HfO2 offers a promising route to reducing Ec. However, the atomic-scale mechanisms driving this behavior remain incompletely understood. Here, using phonon analysis combined with density functional theory simulations, we reveal that interstitial doping and compressive strain strengthen the weak trilinear couplings among the phonon modes that condense in the R3m phase and induced additional modes. These enhanced couplings dramatically increase the polarization, enabling switching at a remarkably low Ec. Our first-principles simulations show that the polarization response strongly depends on the interstitial dopant, as Ti induces large polarization under a slight compressive strain, while Ce, Hf, and Zr require a threshold strain to trigger a polarization jump. Interestingly, we further show that all group-IV interstitial dopants remarkably reduce the Ec under compressive strain. These insights demonstrate that interstitial doping, combined with compressive strain, is a powerful strategy for tuning the ferroelectric properties of HfO2 and offers a promising pathway to enhanced polarization and reduced switching barriers in next-generation ferroelectric devices.