  We study potentially crystalline deformation rings for a residual, ordinary
Galois representation $\overline{\rho}: G_{\mathbb{Q}_p}\rightarrow
\mathrm{GL}_3(\mathbb{F}_p)$. We consider deformations with Hodge-Tate weights
$(0,1,2)$ and inertial type chosen to contain exactly one Fontaine-Laffaille
modular weight for $\overline{\rho}$. We show that, in this setting, the
potentially crystalline deformation space is formally smooth over
$\mathbb{Z}_p$ and any potentially crystalline lift is ordinary. The proof
requires an understanding of the condition imposed by the monodromy operator on
Breuil modules with descent datum, in particular, that this locus mod p is
formally smooth.
