  We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice
and show that it is equivalent to a quantum dimer model on the Kagom\'e
lattice. The model has crystalline confined phases with spontaneously broken
translation invariance associated with pinwheel order, which is investigated
with either a Metropolis or an efficient cluster algorithm. External
half-integer non-Abelian charges (which transform non-trivially under the
$\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other
by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands
of the fractionalized flux strings are domain walls that separate distinct
pinwheel phases. A second-order phase transition in the 3-d Ising universality
class separates two confining phases; one with correlated pinwheel
orientations, and the other with uncorrelated pinwheel orientations.
