We present Young Supernova Experiment grizy photometry of SN 2021hpr, the third Type Ia supernova sibling to explode in the Cepheid calibrator galaxy, NGC 3147. Siblings are useful for improving SN-host distance estimates and investigating their contributions toward the SN Ia intrinsic scatter (post-standardization residual scatter in distance estimates). We thus develop a principled Bayesian framework for analyzing SN Ia siblings. At its core is the cosmology-independent relative intrinsic scatter parameter, σ
Rel: the dispersion of siblings distance estimates relative to one another within a galaxy. It quantifies the contribution toward the total intrinsic scatter, σ
0, from within-galaxy variations about the siblings’ common properties. It also affects the combined distance uncertainty. We present analytic formulae for computing a σ
Rel posterior from individual siblings distances (estimated using any SN model). Applying a newly trained BayeSN model, we fit the light curves of each sibling in NGC 3147 individually, to yield consistent distance estimates. However, the wide σ
Rel posterior means σ
Rel ≈ σ
0 is not ruled out. We thus combine the distances by marginalizing over σ
Rel with an informative prior: σ
Rel ∼ U(0, σ
0). Simultaneously fitting the trio’s light curves improves constraints on distance and each sibling’s individual dust parameters, compared to individual fits. Higher correlation also tightens dust parameter constraints. Therefore, σ
Rel marginalization yields robust estimates of siblings distances for cosmology, as well as dust parameters for sibling–host correlation studies. Incorporating NGC 3147's Cepheid distance yields H
0 = 78.4 ± 6.5 km s−1 Mpc−1. Our work motivates analyses of homogeneous siblings samples, to constrain σ
Rel and its SN-model dependence.