This manuscript presents a relativistic radiative hydrodynamic framework for the Nuclear Impact Hypothesis. The hypothesis proposes that a hypervelocity nuclear aggregate impactor ($v_0 \gtrsim 10^3$ km s$^{-1}$) could trigger proto-solar ignition and eject nascent planetary embryos via asymmetric magnetocentrifugal thrust in a radiation-dominated proto-stellar environment. The model combines Poisson's equation for gravitational potentials, special relativistic momentum conservation, Lorentz forces in magnetized plasmas, three-temperature radiation hydrodynamics, and relativistic Rankine-Hugoniot shock relations, applicable to various stellar configurations. Simulations employ high-resolution cubic interpolation of Standard Solar Model (SSM) profiles constrained by helioseismology (deviations $\lesssim 8\%$). These indicate penetration depths $\delta \approx 0.05 R_\odot$ before electromagnetic disassembly and ablation-mediated fragmentation in neutral proto-stellar cores, achieved through refined modeling of relativistic drag and disassembly criteria. The ejection mechanism involves magnetocentrifugal thrust $a_\mathrm{thrust} = \omega^2 r (B^2 / 4\pi \rho) \gtrsim 10^{-3} c^2 / R_\odot$, driven by proto-stellar rotation and magnetism, leading to escape from $r_0 = 0.1 R_\odot$ at velocities $v_\infty \sim 40$ km s$^{-1}$. These velocities align with orbital circularization and radiative equilibration timescales in typical systems. Variance-based global Sobol sensitivity analysis ($N=2048$) highlights the dominance of initial velocity ($S_{v_0}=0.65$) and thrust ($S_{a_\mathrm{thrust}}=0.58$), with second-order interactions $V_{ij} \approx 0.05$. Bayesian propagation gives $\mu_\delta = 0.048 \pm 0.012 R_\odot$. Falsifiability relies on expected Gaia DR4 transients and meteoritic isotopic disequilibria. Grounded in solar wind plasma diagnostics \cite{kasper2016sweap} and relativistic merger hydrodynamics \cite{hu2024energetic,chan2024distinct}, the framework predicts shock-induced thermonuclear ignition ($\dot{E}_\mathrm{diss} \sim 10^{22}$ erg cm$^{-3}$ s$^{-1}$) and density-selective embryo expulsion ($\rho > 10$ g cm$^{-3}$). It offers insights into Solar System formation and resilience for interstellar probes.