  This article is a continuation of [Kub18], which proves that if a
$3$-dimensional affine normal quasihomogeneous $SL(2)$-variety $E$ is toric,
then it has an equivariant resolution of singularities given by an invariant
Hilbert scheme $\mathcal H$. In this article, we consider the case where $E$ is
non-toric and show that the Hilbert-Chow morphism $\gamma : \mathcal H \to E$
is a resolution of singularities and that $\mathcal H$ is isomorphic to the
minimal resolution of a weighted blow-up of $E$.
