  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 the contributions towards the SN Ia intrinsic scatter
(post-standardisation 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, $\sigma_{Rel}$:
the dispersion of siblings distance estimates relative to one another within a
galaxy. It quantifies the contribution towards the total intrinsic scatter,
$\sigma_0$, from within-galaxy variations about the siblings' common
properties. It also affects the combined-distance uncertainty. We present
analytic formulae for computing a $\sigma_{Rel}$-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
$\sigma_{Rel}$-posterior means $\sigma_{Rel}\approx\sigma_0$ is not ruled out.
We thus combine the distances by marginalizing over $\sigma_{Rel}$ with an
informative prior: $\sigma_{Rel}\sim U(0,\sigma_0)$. 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,
$\sigma_{Rel}$-marginalization yields robust estimates of siblings distances
for cosmology, and dust parameters for siblings-host correlation studies.
Incorporating NGC 3147's Cepheid-distance yields $H_0=78.4\pm 6.5\,$km/s/Mpc.
Our work motivates analyses of homogeneous siblings samples, to constrain
$\sigma_{Rel}$, and its SN-model dependence.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Astrophysical Phenomena