  Let $\Gamma$ be a connected, triangle-free, planar graph with at least five
vertices that has no separating vertices or edges. If the graph $\Gamma$ is
$\mathcal{CFS}$, we prove that the right-angled Coxeter group $G_\Gamma$ is
virtually a Seifert manifold group or virtually a graph manifold group and we
give a complete quasi-isometry classification of these such groups. Otherwise,
we prove that $G_\Gamma$ is hyperbolic relative to a collection of
$\mathcal{CFS}$ right-angled Coxeter subgroups of $G_\Gamma$. Consequently, the
divergence of $G_\Gamma$ is linear, or quadratic, or exponential. We also
generalize right-angled Coxeter groups which are virtually graph manifold
groups to certain high dimensional right-angled Coxeter groups (our families
exist in every dimension) and study the coarse geometry of this collection. We
prove that strongly quasiconvex torsion free infinite index subgroups in
certain graph of groups are free and we apply this result to our right-angled
Coxeter groups.
